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Selftaught rocket scientist/daredevil "Mad" Mike Hughes will finally launch his homemade rocket in two weeks  despite "anonymous online haters questioning his every move." An anonymous reader quotes PhillyVoice: He's found some private land in the "ghost town" of Amboy, California  complete with a brandspankingnew road that'll enable him to get his motor home and rocket gear to the site... "It'll be a vertical launch, me strapped into the rocket with 6,000 pounds of thrust, going up about threeeighths of a mile," he said, noting it's a prologue to a major launch this Fourth of July weekend. "It's the ultimate Wile E. Coyote move." As with the scrubbed mission, this is in part an event which he hopes will get people to investigate the ideology which holds the earth is flat  despite quite a bit of evidence to the contrary. He said it would've happened back in November if international publicity hadn't prompted government bureaucrats to "cover their asses" by pointing out that
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An anonymous reader quotes the EFF: The Electronic Frontier Foundation (EFF) and mobile security company Lookout have uncovered a new malware espionage campaign infecting thousands of people in more than 20 countries. Hundreds of gigabytes of data has been stolen, primarily through mobile devices compromised by fake secure messaging clients. The trojanized apps, including Signal and WhatsApp, function like the legitimate apps and send and receive messages normally. However, the fake apps also allow the attackers to take photos, retrieve location information, capture audio, and more. The threat, called Dark Caracal by EFF and Lookout researchers, may be a nationstate actor and appears to employ shared infrastructure which has been linked to other nationstate actors. In a new report, EFF and Lookout trace Dark Caracal to a building belonging to the Lebanese General Security Directorate in Beirut. "People in the U.S., Canada, Germany, Lebanon, and France have been hit by Dark Caracal. T
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In this paper, the optimal power flow (OPF) problem is augmented to account for the costs associated with the loadfollowing control of a power network. Loadfollowing control costs are expressed through the linear quadratic regulator (LQR). The power network is described by a set of nonlinear differential algebraic equations (DAEs). By linearizing the DAEs around a known equilibrium, a linearized OPF that accounts for steadystate operational constraints is formulated first. This linearized OPF is then augmented by a set of linear matrix inequalities that are algebraically equivalent to the implementation of an LQR controller. The resulting formulation, termed LQROPF, is a semidefinite program which furnishes optimal steadystate setpoints and an optimal feedback law to steer the system to the new steady state with minimum loadfollowing control costs. Numerical tests demonstrate that the setpoints computed by LQROPF result in lower overall costs and frequency deviations compared to
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We extend results of ColliotTh\'el\`ene and Raskind on the $\mathcal{K}_2$cohomology of smooth projective varieties over a separably closed field $k$ to the \'etale motivic cohomology of smooth, not necessarily projective, varieties over $k$. Some consequences are drawn, such as the degeneration of the BlochLichtenbaum spectral sequence for any field containing $k$.
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The purpose of this work is to incorporate numerically, in a discontinuous Galerkin (DG) solver of a BoltzmannPoisson model for hot electron transport, an electronic conduction band whose values are obtained by the spherical averaging of the full band structure given by a local empirical pseudopotential method (EPM) around a local minimum of the conduction band for silicon, as a midpoint between a radial band model and an anisotropic full band, in order to provide a more accurate physical description of the electron group velocity and conduction energy band structure in a semiconductor. This gives a better quantitative description of the transport and collision phenomena that fundamentally define the behaviour of the Boltzmann  Poisson model for electron transport used in this work. The numerical values of the derivatives of this conduction energy band, needed for the description of the electron group velocity, are obtained by means of a cubic spline interpolation. The EPMBoltzmann
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The direct sampling method (DSM) has been introduced for noniterative imaging of small inhomogeneities and is known to be fast, robust, and effective for inverse scattering problems. However, to the best of our knowledge, a full analysis of the behavior of the DSM has not been provided yet. Such an analysis is proposed here within the framework of the asymptotic hypothesis in the 2D case leading to the expression of the DSM indicator function in terms of the Bessel function of order zero and the sizes, shapes and permittivities of the inhomogeneities. Thanks to this analytical expression the limitations of the DSM method when one of the inhomogeneities is smaller and/or has lower permittivity than the others is exhibited and illustrated. An improved DSM is proposed to overcome this intrinsic limitation in the case of multiple incident waves. Then we show that both the traditional and improved DSM are closely related to a normalized version of the Kirchhoff migration. The theoretical e
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Multilayered artificial neural networks are becoming a pervasive tool in a host of application fields. At the heart of this deep learning revolution are familiar concepts from applied and computational mathematics; notably, in calculus, approximation theory, optimization and linear algebra. This article provides a very brief introduction to the basic ideas that underlie deep learning from an applied mathematics perspective. Our target audience includes postgraduate and final year undergraduate students in mathematics who are keen to learn about the area. The article may also be useful for instructors in mathematics who wish to enliven their classes with references to the application of deep learning techniques. We focus on three fundamental questions: what is a deep neural network? how is a network trained? what is the stochastic gradient method? We illustrate the ideas with a short MATLAB code that sets up and trains a network. We also show the use of stateofthe art software on a la
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We develop a cut finite element method (CutFEM) for the convection problem in a so called fractured domain which is a union of manifolds of different dimensions such that a $d$ dimensional component always resides on the boundary of a $d+1$ dimensional component. This type of domain can for instance be used to model porous media with embedded fractures that may intersect. The convection problem can be formulated in a compact form suitable for analysis using natural abstract directional derivative and divergence operators. The cut finite element method is based on using a fixed background mesh that covers the domain and the manifolds are allowed to cut through a fixed background mesh in an arbitrary way. We consider a simple method based on continuous piecewise linear elements together with weak enforcement of the coupling conditions and stabilization. We prove a priori error estimates and present illustrating numerical examples.
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We obtain a new bound on the number of tworich points spanned by an arrangement of low degree algebraic curves in $\mathbb{R}^4$. Specifically, we show that an arrangement of $n$ algebraic curves determines at most $C_\epsilon n^{4/3+3\epsilon}$ tworich points, provided at most $n^{2/3+2\epsilon}$ curves lie in any low degree hypersurface and at most $n^{1/3+\epsilon}$ curves lie in any low degree surface. This result follows from a structure theorem about arrangements of curves that determine many tworich points.
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Fluid queues are mathematical models frequently used in stochastic modelling. Their stationary distributions involve a key matrix recording the conditional probabilities of returning to an initial level from above, often known in the literature as the matrix $\Psi$. Here, we present a probabilistic interpretation of the family of algorithms known as \emph{doubling}, which are currently the most effective algorithms for computing the return probability matrix $\Psi$. To this end, we first revisit the links described in \cite{ram99, soares02} between fluid queues and QuasiBirthDeath processes; in particular, we give new probabilistic interpretations for these connections. We generalize this framework to give a probabilistic meaning for the initial step of doubling algorithms, and include also an interpretation for the iterative step of these algorithms. Our work is the first probabilistic interpretation available for doubling algorithms.
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In 2016, Y\"uce and Torunbalc\i\ Ayd\i n \cite{YucTor} defined dual Fibonacci quaternions. In this paper, we defined the dual thirdorder Jacobsthal quaternions and dual thirdorder JacobsthalLucas quaternions. Also, we investigated the relations between the dual thirdorder Jacobsthal quaternions and thirdorder Jacobsthal numbers. Furthermore, we gave some their quadratic properties, the summations, the Binet's formulas and Cassinilike identities for these quaternions.
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Quadric hypersurfaces are wellknown to satisfy the Hasse principle. However, this is no longer true in the case of the Hasse principle for integral points, where counterexamples are known to exist in dimension 1 and 2. This work explores the frequency that such counterexamples arise in a family of affine quadric surfaces defined over the integers.
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We present a numerical algorithm for evaluating the Boltzmann collision operator with $O(N^2)$ operations based on high order discontinuous Galerkin discretizations in the velocity variable. To formulate the approach, Galerkin projection of the collision operator is written in the form of a bilinear circular convolution. An application of the discrete Fourier transform allows to rewrite the six fold convolution sum as a three fold weighted convolution sum in the frequency space. The new algorithm is implemented and tested in the spatially homogeneous case, and results in a considerable improvement in speed as compared to the direct evaluation. Simultaneous and separate evaluations of the gain and loss terms of the collision operator were considered. Less numerical error was observed in the conserved quantities with simultaneous evaluation.
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Assume that we observe a sample of size n composed of pdimensional signals, each signal having independent entries drawn from a scaled Poisson distribution with an unknown intensity. We are interested in estimating the sum of the n unknown intensity vectors, under the assumption that most of them coincide with a given 'background' signal. The number s of pdimensional signals different from the background signal plays the role of sparsity and the goal is to leverage this sparsity assumption in order to improve the quality of estimation as compared to the naive estimator that computes the sum of the observed signals. We first introduce the group hard thresholding estimator and analyze its mean squared error measured by the squared Euclidean norm. We establish a nonasymptotic upper bound showing that the risk is at most of the order of {\sigma}^2(sp + s^2sqrt(p)) log^3/2(np). We then establish lower bounds on the minimax risk over a properly defined class of collections of ssparse sign
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The main aim of this paper is to bridge two directions of research generalizing asymptotic density zero sets. This enables to transfer results concerning one direction to the other one. Consider a function $g\colon\omega\to [0,\infty)$ such that $\lim_{n\to\infty}g(n)=\infty$ and $\frac{n}{g(n)}$ does not converge to $0$. Then the family $\mathcal{Z}_g=\{A\subseteq\omega:\ \lim_{n\to\infty}\frac{\text{card}(A\cap n)}{g(n)}=0\}$ is an ideal called simple density ideal (or ideal associated to upper density of weight $g$). We compare this class of ideals with Erd\H{o}sUlam ideals. In particular, we show that there are $\sqsubseteq$antichains of size $\mathfrak{c}$ among Erd\H{o}sUlam ideals which are and are not simple density ideals. We characterize simple density ideals which are Erd\H{o}sUlam as those containing the classical ideal of sets of asymptotic density zero. We also characterize Erd\H{o}sUlam ideals which are simple density ideals. In the latter case we need to introduce
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We obtain sufficient criteria for endomorphisms of torsionfree nilpotent groups of finite rank to be automorphisms, by considering the induced maps on the torsionfree abelianisation and the centre. Whilst these results are known in the finitely generated case removing this assumption introduces several difficulties.
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This paper introduces a new fast algorithm for the 8point discrete cosine transform (DCT) based on the summationbyparts formula. The proposed method converts the DCT matrix into an alternative transformation matrix that can be decomposed into sparse matrices of low multiplicative complexity. The method is capable of scaled and exact DCT computation and its associated fast algorithm achieves the theoretical minimal multiplicative complexity for the 8point DCT. Depending on the nature of the input signal simplifications can be introduced and the overall complexity of the proposed algorithm can be further reduced. Several types of input signal are analyzed: arbitrary, null mean, accumulated, and null mean/accumulated signal. The proposed tool has potential application in harmonic detection, image enhancement, and feature extraction, where input signal DC level is discarded and/or the signal is required to be integrated.
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An anonymous reader quotes SiliconBeat: Santa Clara autotech firm Telenav has just announced an "incar advertising platform" for cars that connect to the internet. Telenav wants to sell the system to major auto manufacturers. And although it's probably the last thing many consumers want, vehicle owners will pay more for connectedcar services if they decline the ads. "This approach helps car makers offset costs related to connected services, such as wireless data, content, software and cloud services," a spokeswoman for Telenav said Jan. 5. "In return for accepting ads in vehicles, drivers benefit from access to connected services without subscription fees, as well as new driving experiences that come from the highlytargeted and relevant offers delivered based on information coming from the vehicle." Auto makers including Toyota, Lexus, Ford, GM and Cadillac already use the company's connectedcar products, the spokeswoman said. Telenav CEO H.P. Jin in a press release called the ad
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An anonymous reader quotes a report from The Verge: Amid vocal calls for the company to act, Twitter today offered its first explanation for why it hasn't banned President Donald Trump  without ever saying the man's name. "Elected world leaders play a critical role in that conversation because of their outsized impact on our society," the company said in a blog post. "Blocking a world leader from Twitter or removing their controversial Tweets, would hide important information people should be able to see and debate. It would also not silence that leader, but it would certainly hamper necessary discussion around their words and actions." In its blog post, Twitter reiterated its previous statement that all accounts still must follow the company's rules. The statement seemed to leave open the possibility that it might one day take action against Trump's account, or the accounts of other world leaders who might use the platform to incite violence or otherwise break its rules. "We review
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In the sparse normal means model, convergence of the Bayesian posterior distribution associated to spike and slab prior distributions is considered. The key sparsity hyperparameter is calibrated via marginal maximum likelihood empirical Bayes. The plugin posterior squared$L^2$ norm is shown to converge at the minimax rate for the euclidean norm for appropriate choices of spike and slab distributions. Possible choices include standard spike and slab with heavy tailed slab, and the spike and slab LASSO of Rockov\'a and George with heavy tailed slab. Surprisingly, the popular Laplace slab is shown to lead to a suboptimal rate for the full empirical Bayes posterior. This provides a striking example where convergence of aspects of the empirical Bayes posterior does not entail convergence of the full empirical Bayes posterior itself.
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The split control and user plane is key to the future heterogeneous cellular network (HCN), where the small cells are dedicated for the most data transmission while the macrocells are mainly responsible for the control signaling. Adapting to this technology, we propose a general and tractable framework of extra cell range expansion (CRE) by introducing an additional bias factor to enlarge the range of small cells flexibly for the extra offloaded macrousers in a twotier HCN, where the macrocell and small cell users have different required data rates. Using stochastic geometry, we analyze the energy efficiency (EE) of the extra CRE with joint low power transmission and resource partitioning, where the coverages of EE and data rate are formulated theoretically. Numerical simulations verify that the proposed extra CRE can improve the EE performance of HCN, and also show that deploying more small cells can provide benefits for EE coverage, but the EE improvement becomes saturated if the sm
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Coordinated multipoint (CoMP) joint transmission (JT) can save a great deal of energy especially for celledge users due to strengthened received signal, but at the cost of deploying and coordinating cooperative nodes, which degrades energy efficiency (EE), particularly when considerable amount of energy is consumed by nonideal hardware circuit. In this paper, we study energyefficient cooperation establishment, including cooperative nodes selection (CNS) and power allocation, to satisfy a required data rate in coherent JTCoMP networks with nonideal power amplifiers (PAs) and circuit power. The selection priority lemma is proved first, and then the formulated discrete combinatorial EE optimization is resolved by proposing node selection criterion and deriving closedform expressions of optimal transmission power. Therefore, an efficient algorithm is provided and its superiority is validated by Monte Carlo simulations, which also show the effects of nonideal PA and the data rate demand
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In this paper, we maximize the energy efficiency (EE) of fullduplex (FD) twoway relay (TWR) systems under nonideal power amplifiers (PAs) and nonnegligible transmissiondependent circuit power. We start with the case where only the relay operates full duplex and two timeslots are required for TWR. Then, we extend to the advanced case, where the relay and the two nodes all operate full duplex, and accomplish TWR in a single timeslot. In both cases, we establish the intrinsic connections between the optimal transmit powers and durations, based on which the original nonconvex EE maximization can be convexified and optimally solved. Simulations show the superiority of FDTWR in terms of EE, especially when traffic demand is high. The simulations also reveal that the maximum EE of FDTWR is more sensitive to the PA efficiency, than it is to selfcancellation. The full FD design of FDTWR is susceptible to traffic imbalance, while the design with only the relay operating in the FD mode
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An anonymous reader quotes Fortune's new report on blockchain: Demand for the technology, best known for supporting bitcoin, is growing so much that it will be one of the largest users of capacity next year at about 60 data centers that IBM rents out to other companies around the globe. IBM was one of the first big companies to see blockchain's promise, contributing code to an opensource effort and encouraging startups to try the technology on its cloud for free. That a 106yearold company like IBM is going all in on blockchain shows just how far the digital ledger has come since its early days underpinning bitcoin drug deals on the dark web. The market for blockchainrelated products and services will reach $7.7 billion in 2022, up from $242 million last year, according to researcher Markets & Markets. That's creating new opportunities for some of the old warships of the technology world, companies like IBM and Microsoft Corp. that are making the transition to cloud services. A
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The CEO of Wireline  a cloud application marketplace and serverless architecture platform  is pushing for an open source development fund to help sustain projects, funded by an initial coin offering. "Developers like me know that there are a lot of weak spots in the modern internet," he writes on MarketWatch, suggesting more Equifaxsized data breaches may wait in our future. In fact, many companies are not fully aware of all of the software components they are using from the opensource community. And vulnerabilities can be left open for years, giving hackers opportunities to do their worst. Take, for instance, the Heartbleed bug of 2014... Among the known hacks: 4.5 million healthcare records were compromised, 900 Canadians' social insurance numbers were stolen. It was deemed "catastrophic." And yet many servers today  two years later!  still carry the vulnerability, leaving whole caches of personal data exposed... [T]hose of us who are on the back end, stitching away, ofte
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schwit1 shares a report from The Daily Dot: A man was killed by police Thursday night in Wichita, Kansas, when officers responded to a false report of a hostage situation. The online gaming community is saying the dead man was the victim of a swatting prank, where trolls call in a fake emergency and force SWAT teams to descend on a target's house. If that's true, this would be the first reported swattingrelated death. Wichita deputy police chief Troy Livingston told the Wichita Eagle that police were responding to a report that a man fighting with his parents had accidentally shot his dad in the head and was holding his mom, brother and sister hostage. When police arrived, "A male came to the front door," Livingston told the Eagle. "As he came to the front door, one of our officers discharged his weapon." The man at the door was identified by the Eagle as 28yearold Andrew Finch. Finch's mother told reporters "he was not a gamer," but the online Call of Duty community claims his deat
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Combined, Disney and Lucasfilm's Star Wars: The Last Jedi, Rogue One: A Star Wars Story and Star Wars: The Force Awakens have surpassed $4.06 billion in ticket sales at the worldwide box office. That's more than what Disney paid to buy George Lucas' Star Wars franchise. From the Hollywood Reporter: While an interesting benchmark, it doesn't, of course, account for the hundreds of millions spent to produce and market the trio of films, or the fact that Disney splits boxoffice grosses with theater owners. Conversely, Disney has minted additional money from lucrative ancillary revenue streams, merchandising sales and theme park attractions. Opening in North America on Dec. 15, The Last Jedi zoomed past the $900 million mark on Thursday, finishing the day with $934.2 million globally, including $464.6 million domestically and $469.6 internationally (it doesn't land in China until Jan. 5). The sequel to The Force Awakens was directed by Rian Johnson, and has dominated the Christmas corrido
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An anonymous reader quotes a report from The Guardian: Britain's homes could be lit and powered by wind farms surrounding an artificial island deep out in the North Sea, under advanced plans by a Dutch energy network. The radical proposal envisages an island being built to act as a hub for vast offshore wind farms that would eclipse today's facilities in scale. Dogger Bank, 125km (78 miles) off the East Yorkshire coast, has been identified as a potentially windy and shallow site. The power hub would send electricity over a longdistance cable to the UK and Netherlands, and possibly later to Belgium, Germany, and Denmark. TenneT, the project's backer and Dutch equivalent of the UK's National Grid, recently shared early findings of a study that said its plan could be billions of euros cheaper than conventional wind farms and international power cables. The scifisounding proposal is sold as an innovative answer to industry's challenge of continuing to make offshore wind cheaper, as turb
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We show that for any positive integer k, the kth nonzero eigenvalue of the LaplaceBeltrami operator on the twodimensional sphere endowed with a Riemannian metric of unit area, is maximized in the limit by a sequence of metrics converging to a union of k touching identical round spheres. This proves a conjecture posed by the second author in 2002 and yields a sharp isoperimetric inequality for all nonzero eigenvalues of the Laplacian on a sphere. Earlier, the result was known only for k=1 (J.Hersch, 1970), k=2 (N.Nadirashvili, 2002 and R.Petrides, 2014) and k=3 (N.Nadirashvili and Y.Sire, 2015). In particular, we argue that for any k>=2, the supremum of the kth nonzero eigenvalue on a sphere of unit area is not attained in the class of Riemannin metrics which are smooth outsitde a finite set of conical singularities. The proof uses certain properties of harmonic maps between spheres, the key new ingredient being a bound on the harmonic degree of a harmonic map into a sphere obtai
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We provide a number of extensions and further interpretations of the ParameterizedBackground DataWeak (PBDW) formulation, a realtime and insitu Data Assimilation (DA) framework for physical systems modeled by parametrized Partial Differential Equations (PDEs), proposed in [Y Maday, AT Patera, JD Penn, M Yano, Int J Numer Meth Eng, 102(5), 933965]. Given $M$ noisy measurements of the state, PBDW seeks an approximation of the form $u^{\star} = z^{\star} + \eta^{\star}$, where the \emph{background} $z^{\star}$ belongs to a $N$dimensional \emph{background space} informed by a parameterized mathematical model, and the \emph{update} $\eta^{\star}$ belongs to a $M$dimensional \emph{update space} informed by the experimental observations. The contributions of the present work are threefold: first, we extend the adaptive formulation proposed in [T Taddei, M2AN, 51(5), 18271858] to general linear observation functionals, to effectively deal with noisy observations; second, we consider an
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We extend the standard Bayesian multivariate Gaussian generative data classifier by considering a generalization of the conjugate, normalWishart prior distribution and by deriving the hyperparameters analytically via evidence maximization. The behaviour of the optimal hyperparameters is explored in the highdimensional data regime. The classification accuracy of the resulting generalized model is competitive with stateofthe art Bayesian discriminant analysis methods, but without the usual computational burden of crossvalidation.
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Fully localised solitary waves are travellingwave solutions of the threedimensional gravitycapillary water wave problem which decay to zero in every horizontal spatial direction. Their existence has been predicted on the basis of numerical simulations and model equations (in which context they are usually referred to as `lumps'), and a mathematically rigorous existence theory for strong surface tension (Bond number $\beta$ greater than $\frac{1}{3}$) has recently been given. In this article we present an existence theory for the physically more realistic case $0<\beta<\frac{1}{3}$. A classical variational principle for fully localised solitary waves is reduced to a locally equivalent variational principle featuring a perturbation of the functional associated with the DaveyStewartson equation. A nontrivial critical point of the reduced functional is found by minimising it over its natural constraint set.
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In this paper, we study an interference avoidance scenario in the presence of a smart interferer which can rapidly observe the transmit power of a backscatter wireless sensor network (WSN) and effectively interrupt backscatter signals. We consider a power control with a subchannel allocation to avoid interference attacks and a timeswitching ratio for backscattering and RF energy harvesting in backscatter WSNs. We formulate the problem based on a Stackelberg game theory and compute the optimal transmit power, timeswitching ratio, and subchannel allocation parameter to maximize a utility function against the smart interference. We propose two algorithms for the utility maximization using Lagrangian dual decomposition for the backscatter WSN and the smart interference to prove the existence of the Stackelberg equilibrium. Numerical results show that the proposed algorithms effectively maximize the utility, compared to that of the algorithm based on the Nash game, so as to overcome sma
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We propose a new practical adaptive refinement strategy for $hp$finite element approximations of elliptic problems. Following recent theoretical developments in polynomialdegreerobust a posteriori error analysis, we solve two types of discrete local problems on vertexbased patches. The first type involves the solution on each patch of a mixed finite element problem with homogeneous Neumann boundary conditions, which leads to an ${\mathbf H}(\mathrm{div},\Omega)$conforming equilibrated flux. This, in turn, yields a guaranteed upper bound on the error and serves to mark mesh vertices for refinement via D\"orfler's bulkchasing criterion. The second type of local problems involves the solution, on patches associated with marked vertices only, of two separate primal finite element problems with homogeneous Dirichlet boundary conditions, which serve to decide between $h$, $p$, or $hp$refinement. Altogether, we show that these ingredients lead to a computable guaranteed bound on the
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We consider three problems about cities from Alcuin's_Propositiones ad acuendos juvenes_. These problems can be considered as the earliest packing problems difficult also for modern stateoftheart packing algorithms. We discuss the Alcuin's solutions and give the known (to the author) best solutions to these problems.
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In this article we use the combinatorial and geometric structure of manifolds with embedded cylinders in order to develop an adiabatic decomposition of the Hodge cohomology of these manifolds. We will on the one hand describe the adiabatic behaviour of spaces of harmonic forms by means of a certain \v{C}echde Rham complex and on the other hand generalise the CappellLeeMiller splicing map to the case of a finite number of edges, thus combining the topological and the analytic viewpoint. In parts, this work is a generalisation of works of Cappell, Lee and Miller in which a singleedged graph is considered, but it is more specific since only the GaussBonnet operator is studied.
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We study the automorphism groups of countable homogeneous directed graphs (and some additional homogeneous structures) from the point of view of topological dynamics. We determine precisely which of these automorphism groups are amenable (in their natural topologies). For those which are amenable, we determine whether they are uniquely ergodic, leaving unsettled precisely one case (the "semigeneric" complete multipartite directed graph). We also consider the Hrushovski property. For most of our results we use the various techniques of [3], suitably generalized to a context in which the universal minimal flow is not necessarily the space of all orders. Negative results concerning amenability rely on constructions of the type considered in [26]. An additional class of structures (compositions) may be handled directly on the basis of very general principles. The starting point in all cases is the determination of the universal minimal flow for the automorphism group, which in the context
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We consider a variational problem associated with the minimal speed of pulsating traveling waves of the equation $u_t=u_{xx}+b(x)(1u)u$, $x\in{\mathbb R},\ t>0$, where the coefficient $b(x)$ is nonnegative and periodic in $x\in{\mathbb R}$ with a period $L>0$. It is known that there exists a quantity $c^*(b)>0$ such that a pulsating traveling wave with the average speed $c>0$ exists if and only if $c\geq c^*(b)$. The quantity $c^*(b)$ is the socalled minimal speed of pulsating traveling waves. In this paper, we study the problem of maximizing $c^*(b)$ by varying the coefficient $b(x)$ under some constraints. We prove the existence of the maximizer under a certain assumption of the constraint and derive the EulerLagrange equation which the maximizer satisfies under $L^2$ constraint $\int_0^L b(x)^2dx=\beta$. The limit problems of the solution of this EulerLagrange equation as $L\rightarrow0$ and as $\beta\rightarrow0$ are also considered. Moreover, we also consider the
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In this paper and upcoming ones, we initiate a systematic study of Bethe ansatz equations for integrable models by modern computational algebraic geometry. We show that algebraic geometry provides a natural mathematical language and powerful tools for understanding the structure of solution space of Bethe ansatz equations. In particular, we find novel efficient methods to count the number of solutions of Bethe ansatz equations based on Gr\"obner basis and quotient ring. We also develop analytical approach based on companion matrix to perform the sum of onshell quantities over all physical solutions without solving Bethe ansatz equations explicitly. To demonstrate the power of our method, we revisit the completeness problem of Bethe ansatz of Heisenberg spin chain, and calculate the sum rules of OPE coefficients in planar $\mathcal{N}=4$ superYangMills theory.
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We present a novel approach to hybrid RANS/LES wall modeling based on function enrichment, which overcomes the common problem of the RANSLES transition and enables coarse meshes near the boundary. While the concept of function enrichment as an efficient discretization technique for turbulent boundary layers has been proposed in an earlier article by Krank & Wall (J. Comput. Phys. 316 (2016) 94116), the contribution of this work is a rigorous derivation of a new multiscale turbulence modeling approach and a corresponding discontinuous Galerkin discretization scheme. In the nearwall area, the NavierStokes equations are explicitly solved for an LES and a RANS component in one single equation. This is done by providing the Galerkin method with an independent set of shape functions for each of these two methods; the standard highorder polynomial basis resolves turbulent eddies where the mesh is sufficiently fine and the enrichment automatically computes the ensembleaveraged flow i
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We describe a paradigm for multiscale modeling that combines the MoriZwanzig (MZ) formalism of Statistical Mechanics with the Variational Multiscale (VMS) method. The MZVMS approach leverages both VMS scaleseparation projectors as well as phasespace projectors to provide a systematic modeling approach that is applicable to nonlinear partial differential equations. Spectral as well as continuous and discontinuous finite element methods are considered. The framework leads to a formally closed equation in which the effect of the unresolved scales on the resolved scales is nonlocal in time and appears as a convolution or memory integral. The resulting nonMarkovian system is used as a starting point for model development. We discover that unresolved scales lead to memory effects that are driven by an orthogonal projection of the coarsescale residual and interelement jumps. It is further shown that an MZbased finite memory model is a variant of the wellknown adjointstabilization
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We consider the classic problem of network reliability. A network is given together with a source vertex, one or more target vertices and probabilities assigned to each of the edges. Each edge appears in the network with its associated probability and the problem is to determine the probability of having at least one sourcetotarget path. This problem is known to be NPhard for general networks and has been solved for several special families. In this work we present a fixedparameter algorithm based on treewidth, which is a measure of treelikeness of graphs. The problem was already known to be solvable in linear time for bounded treewidth, however the known methods used complicated structures and were not easy to implement. We provide a significantly simpler and more intuitive algorithm that while remaining linear, is much easier to implement.
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Analyzing the security of cryptosystems under attacks based on the malicious modification of memory registers is a research topic of high importance. This type of attacks may affect the randomness of the secret parameters by forcing a limited number of bits to a certain value which can be unknown to the attacker. In this context, we revisit the attack on DSA presented by Faug\`ere, Goyet and Renault during the conference SAC 2012: we simplify their method and we provide a probabilistic approach in opposition to the heuristic proposed in the former to measure the limits of the attack. More precisely, the main problem is formulated as the search for a closest vector to a lattice, then we study the distribution of the vectors with bounded norms in a this family of lattices and we apply the result to predict the behavior of the attack. We validated this approach by computational experiments.
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In this paper we study the complexity of constructing a hitting set for the closure of VP, the class of polynomials that can be infinitesimally approximated by polynomials that are computed by polynomial sized algebraic circuits, over the real or complex numbers. Specifically, we show that there is a PSPACE algorithm that given n,s,r in unary outputs a set of ntuples over the rationals of size poly(n,s,r), with poly(n,s,r) bit complexity, that hits all nvariate polynomials of degreer that are the limit of sizes algebraic circuits. Previously it was known that a random set of this size is a hitting set, but a construction that is certified to work was only known in EXPSPACE (or EXPH assuming the generalized Riemann hypothesis). As a corollary we get that a host of other algebraic problems such as Noether Normalization Lemma, can also be solved in PSPACE deterministically, where earlier only randomized algorithms and EXPSPACE algorithms (or EXPH assuming the generalized Riemann hypot
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This work pioneers the systematic study and classification (up to Lie algebra automorphisms) of finitedimensional coboundary Lie bialgebras through Grassmann algebras. Several mathematical structures on Lie algebras, e.g. Killing forms or root decompositions, are extended to the Grassmann algebras of Lie algebras. This simplifies the description of the procedures and tools appearing in the theory of Lie bialgebras and originates novel techniques for its study and classification up to Lie algebra automorphisms. As a particular case, the classification of real threedimensional coboundary Lie bialgebras is retrieved.
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\emph{Multiresolution mode decomposition} (MMD) is an adaptive tool to analyze a time series $f(t)=\sum_{k=1}^K f_k(t)$, where $f_k(t)$ is a \emph{multiresolution intrinsic mode function} (MIMF) of the form \begin{eqnarray*} f_k(t)&=&\sum_{n=N/2}^{N/21} a_{n,k}\cos(2\pi n\phi_k(t))s_{cn,k}(2\pi N_k\phi_k(t))\\&&+\sum_{n=N/2}^{N/21}b_{n,k} \sin(2\pi n\phi_k(t))s_{sn,k}(2\pi N_k\phi_k(t)) \end{eqnarray*} with timedependent amplitudes, frequencies, and waveforms. The multiresolution expansion coefficients $\{a_{n,k}\}$, $\{b_{n,k}\}$, and the shape function series $\{s_{cn,k}(t)\}$ and $\{s_{sn,k}(t)\}$ provide innovative features for adaptive time series analysis. The MMD aims at identifying these MIMF's (including their multiresolution expansion coefficients and shape functions series) from their superposition. This paper proposes a fast algorithm for solving the MMD problem based on recursive diffeomorphismbased spectral analysis (RDSA). RDSA admits highly efficie
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