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We use classical results in smoothing theory to extract information about the rational homotopy groups of the space of negatively curved metrics on a high dimensional manifold. It is also shown that smooth Mbundles over spheres equipped with fiberwise negatively curved metrics, represent elements of finite order in the homotopy groups of the classifying space for smooth Mbundles, provided the dimension of M is large enough.
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We discuss magneticelectric fields based finite element schemes for stationary magnetohydrodynamics (MHD) systems with two types of boundary conditions. The schemes are unconditional wellposed and stable. Moreover, magnetic Gauss's law $\nabla\cdot\bm{B}=0$ is preserved precisely on the discrete level. We establish a key $L^{3}$ estimate for divergencefree finite element functions for a new type of boundary condition. With this estimate and a similar one in \cite{hu2015structure}, we rigorously prove the convergence of Picard iterations and the finite element schemes. These results show that the proposed finite element methods converge for singular solutions.
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We introduce a novel unbiased estimator for the density of a sum of random variables. Our estimator possesses several advantages over the conditional Monte Carlo approach. Specifically, it applies to the case of dependent random variables, allows for transformations of random variables, is computationally faster to run, and is simpler to implement. We provide several numerical examples that illustrate these advantages.
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When choosing between candidate nest sites, a honeybee swarm reliably chooses the most valuable site and even when faced with the choice between nearequal value sites, it makes highly efficient decisions. Valuesensitive decisionmaking is enabled by a distributed social effort among the honeybees, and it leads to decisionmaking dynamics of the swarm that are remarkably robust to perturbation and adaptive to change. To explore and generalize these features to other networks, we design distributed multiagent network dynamics that exhibit a pitchfork bifurcation, ubiquitous in biological models of decisionmaking. Using tools of nonlinear dynamics we show how the designed agentbased dynamics recover the high performing valuesensitive decisionmaking of the honeybees and rigorously connect investigation of mechanisms of animal group decisionmaking to systematic, bioinspired control of multiagent network systems. We further present a distributed adaptive bifurcation control law and
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Graded quasicommutative skew PBW extensions are isomorphic to graded iterated Ore extensions of endomorphism type, whence graded quasicommutative skew PBW extensions with coefficients in ASregular algebras are skew CalabiYau and the Nakayama automorphism exists for these extensions. With this in mind, in this paper we give a description of Nakayama automorphism for these noncommutative algebras using the Nakayama automorphism of the ring of the coefficients.
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The decomposability of a Cartesian product of two nondecomposable manifolds into products of lower dimensional manifolds is studied. For 3manifolds we obtain an analog of a result due to Borsuk for surfaces, and in higher dimensions we show that similar analogs do not exist unless one imposes further restrictions such as simple connectivity.
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Complications exist when solving the field equation in the nonlocal field. This has been attributed to the complexity of deriving explicit forms of the nonlocal boundary conditions. Thus, the paradoxes in the existing solutions of the nonlocal field equation have been revealed in recent studies. In the present study, a new methodology is proposed to easily determine the elastic nonlocal fields from their local counterparts without solving the field equation. This methodology depends on the iterativenonlocal residual approach in which the sum of the nonlocal fields is treaded as a residual field. Thus, in this study the corrections of the locallinear elastic fields for the nonlocal residuals in materials are presented. These corrections are formed based on the general nonlocal theory. In the context of the general nonlocal theory, two distinct nonlocal parameters are introduced to form the constitutive equations of isotropiclinear elastic continua. In this study, it is demonstrated t
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We study the distribution of the sequence of elements of the discrete dynamical system generated by the M\"obius transformation $x \mapsto (ax + b)/(cx + d)$ over a finite field of $p$ elements at the moments of time that correspond to prime numbers. Motivated by a recent conjecture of P. Sarnak, we obtain nontrivial estimates of exponential sums with such sequences that imply that trajectories of this dynamical system are disjoined with the M\"obius function. We also obtain an equidistribution result for such trajectories at prime moments of time.
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This paper focuses on the distributed optimal cooperative control for continuoustime nonlinear multiagent systems (MASs) with completely unknown dynamics via adaptive dynamic programming (ADP) technology. By introducing predesigned extra compensators, the augmented neighborhood error systems are derived which successfully circumvents the system knowledge requirement for ADP. It is revealed that the optimal consensus protocols actually work as solutions of the MAS differential game. Policy iteration (PI) algorithm is adopted, and it is theoretically proved that the iterative value function sequence strictly converges to the solution of the coupled HamiltonJacobiBellman (CHJB) equation. Based on this point, a novel online iterative scheme is proposed which runs based on the data sampled from the augmented system and the gradient of the value function. Neural networks (NNs) are employed to implement the algorithm and the weights are updated, in the leastsquare sense, to the ideal val
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We consider the consensual distributed optimization problem in the Riemannian context. Specifically, the minimization of a sum of functions form is studied where each individual function in the sum is located at the node of a network. An algorithm, which is a direct generalization of the Euclidean case, to solve the problem is proposed. The convergence analysis is carried out in full detail for geodesically convex as well as nonconvex functions. The algorithm is demonstrated using some standard applications which fit the presented framework.
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This work studies slice functions over finitedimensional division algebras. Their zero sets are studied in detail along with their multiplicative inverses, for which some unexpected phenomena are discovered. The results are applied to prove some useful properties of the subclass of slice regular functions, previously known only over quaternions. Firstly, they are applied to derive from the maximum modulus principle a version of the minimum modulus principle, which is in turn applied to prove the open mapping theorem. Secondly, they are applied to prove, in the context of the classification of singularities, the counterpart of the CasoratiWeierstrass theorem.
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On the probability simplex, we can consider the standard information geometric structure with the e and maffine connections mutually dual with respect to the Fisher metric. The geometry naturally defines submanifolds simultaneously autoparallel for the both affine connections, which we call {\em doubly autoparallel submanifolds}. In this note we discuss their several interesting common properties. Further, we algebraically characterize doubly autoparallel submanifolds on the probability simplex and give their classification.
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In this paper, the feasibility of a new downlink transmission mode in massive multiinput multioutput (MIMO) systems is investigated with two types of users, i.e., the users with only statistical channel state information (CSI) and the users with imperfect instantaneous CSI. The problem of downlink precoding design with mixed utilization of statistical and imperfect instantaneous CSI is addressed. We first theoretically analyze the impact of the mutual interference between the two types of users on their achievable rate. Then, considering the mutual interference suppression, we propose an extended zeroforcing (eZF) and an extended maximum ratio transmission (eMRT) precoding methods to minimize the total transmit power of base station and to maximize the received signal power of users, respectively. Thanks to the exploitation of statistical CSI, pilotbased channel estimation is avoided enabling more active users, higher system sum rate and shorter transmission delay. Finally, simulat
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We deal with the duality symmetry of the Dilaton field in cosmology and specifically with the socalled GasperiniVeneziano duality transformation. In particular, we determine two conformal equivalent theories to the Dilaton field, and we show that under conformal transformations GasperiniVeneziano duality symmetry does not survive. Moreover, we show that those theories share a common conservation law, of Noetherian kind, while the symmetry vector which generates the conservation law is an isometry only for the Dilaton field. Finally, we show that the Lagrangian of the Dilaton field is equivalent with that of the twodimensional \textquotedblright hyperbolic oscillator\textquotedblright\ in a Lorentzian space whose $O(d,d)$ invariance is transformed to the GasperiniVeneziano duality invariance in the original coordinates.
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Helicity is the scalar product between velocity and vorticity and, just like energy, its integral is an inviscid invariant of the threedimensional incompressible NavierStokes equations. However, spaceand timediscretization methods typically corrupt this property, leading to violation of the inviscid conservation principles. This work investigates the discrete helicity conservation properties of spectral and finitedifferencing methods, in relation to the form employed for the convective term. Effects due to RungeKutta timeadvancement schemes are also taken into consideration in the analysis. The theoretical results are proved against inviscid numerical simulations, while a scaledependent analysis of energy, helicity and their nonlinear transfers is performed to further characterize the discretization errors of the different forms in forced helical turbulence simulations.
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The element distinctness problem is the problem of determining whether the elements of a list are distinct. Classically, it requires $N$ queries, where $N$ is the number of elements. In the quantum case, it is possible to solve the problem in $O(N^{2/3})$ queries. The problem can be extended by asking whether there are $k$ colliding elements, known as element $k$distinctness. This work obtains optimal values of two critical parameters of Ambainis' seminal algorithm [\textit{SIAM Journal on Computing}, 37(1):210239, 2007]. The first critical parameter is the number of repetitions of the algorithm's main block, which inverts the phase of the marked elements and calls a subroutine. The second parameter is the number of quantum walk steps interlaced by oracle queries. We show that, when the optimal values of the parameters are used, the algorithm's success probability is $1O(N^{1/(k+1)})$, quickly approaching to 1.
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A \textit{diameter graph in $\mathbb R^d$} is a graph, whose set of vertices is a finite subset of $\mathbb R^d$ and whose set of edges is formed by pairs of vertices that are at diameter apart. This paper is devoted to the study of different extremal properties of diameter graphs in $\mathbb R^4$ and on a threedimensional sphere. We prove an analogue of V\'azsonyi's and Borsuk's conjecture for diameter graphs on a threedimensional sphere with radius greater than $1/\sqrt 2$. We prove Schur's conjecture for diameter graphs in $\mathbb R^4.$ We also establish the maximum number of triangles a diameter graph in $\mathbb R^4$ can have, showing that the extremum is attained only on specific Lenz configurations.
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Backscatter communication (BackCom), which allows a backscatter node (BN) to communicate with the reader by modulating and reflecting the incident continuous wave from the reader, is considered as a promising solution to power the future InternetofThings. In this paper, we consider a single BackCom system, where multiple BNs are served by a reader. We propose to use the powerdomain nonorthogonal multiple access (NOMA), i.e., multiplexing the BNs in different regions or with different backscattered power levels, to enhance the spectrum efficiency of the BackCom system. To better exploit powerdomain NOMA, we propose to set the reflection coefficients for multiplexed BNs to be different. Based on this considered model, we develop the reflection coefficient selection criteria. To illustrate the enhanced system with the proposed criteria, we analyze the performance of BackCom system in terms of the average number of bits that can be successfully decoded by the reader for twonode pairi
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Let $\mathcal {W}^k(\mathfrak{sl}_4, f_{\text {subreg}})$ be the universal $\mathcal{W}$algebra associated to $\mathfrak{sl}_4$ with its subregular nilpotent element, and let $\mathcal {W}_k(\mathfrak{sl}_4, f_{\text {subreg}})$ be its simple quotient. There is a Heisenberg subalgebra $\mathcal{H}$, and we denote by $\mathcal{C}^k$ the coset $\text{Com}(\mathcal{H}, \mathcal {W}^k(\mathfrak{sl}_4, f_{\text {subreg}}))$, and by $\mathcal{C}_k$ its simple quotient. We show that for $k=4+(m+4)/3$ where $m$ is an integer greater than $2$ and $m+1$ is coprime to $3$, $\mathcal{C}_k$ is isomorphic to a rational, regular $\mathcal W$algebra $\mathcal{W}(\mathfrak{sl}_m, f_{\text{reg}})$. In particular, $\mathcal{W}_k(\mathfrak{sl}_4, f_{\text {subreg}})$ is a simple current extension of the tensor product of $\mathcal{W}(\mathfrak{sl}_m, f_{\text{reg}})$ with a rank one lattice vertex operator algebra, and hence is rational.
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In this work, the classical Borsuk conjecture is discussed, which states that any set of diameter 1 in the Euclidean space $ {\mathbb R}^d $ can be divided into $ d+1 $ parts of smaller diameter. During the last two decades, many counterexamples to the conjecture have been proposed in high dimensions. However, all of them are sets of diameter 1 that lie on spheres whose radii are close to the value $ {1}{\sqrt{2}} $. The main result of this paper is as follows: {\it for any $ r > {1}{2} $, there exists a $ d_0 $ such that for all $ d \ge d_0 $, a counterexample to Borsuk's conjecture can be found on a sphere $ S_r^{d1} \subset {\mathbb R}^d $.
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We investigate a nonhomogeneous nonlinear heat equation which involves degenerate or singular coefficients belonging to the $A_2$ class of functions. We prove the existence of a Fujita exponent and describe the dichotomy existence/nonexistence of global in time solutions. The $A_2$ coefficient admits either a singularity at the origin or a line of singularities. In this latter case, the problem is related to the fractional laplacian, through the CaffarelliSilvestre extension and is a first attempt to develop a parabolic theory in this setting.
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Let $ G $ be a real simple linear connected Lie group of real rank one. Then, $ X := G/K $ is a Riemannian symmetric space with strictly negative sectional curvature. By the classification of these spaces, $X$ is a real/complex/quaternionic hyperbolic space or the Cayley hyperbolic plane. We define the Schwartz space $ \mathscr{C}(\Gamma \backslash G) $ on $ \Gamma \backslash G $ for torsionfree geometrically finite subgroups $ \Gamma $ of $G$. We show that it has a Fr\'echet space structure, that the space of compactly supported smooth functions is dense in this space, that it is contained in $ L^2(\Gamma \backslash G) $ and that the right translation by elements of $G$ defines a representation on $ \mathscr{C}(\Gamma \backslash G) $. Moreover, we define the space of cusp forms $ \deg\mathscr{C}(\Gamma \backslash G) $ on $ \Gamma \backslash G $, which is a geometrically defined subspace of $ \mathscr{C}(\Gamma \backslash G) $. It consists of the Schwartz functions which have vanishin
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We investigate oneparameter deformations of functions on affine space which define parametrizable hyper surfaces. With the assumption of isolated polar activity at the origin, we are able to completely express the L\^e numbers of the special fiber in terms of the L\^e numbers of the generic fiber and the characteristic polar multiplicities of the multiplepoint complex, a perverse sheaf naturally associated to any parameterized hyper surface.
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In Demand Response programs, price incentives might not be sufficient to modify residential consumers load profile. Here, we consider that each consumer has a preferred profile and a discomfort cost when deviating from it. Consumers can value this discomfort at a varying level that we take as a parameter. This work analyses Demand Response as a game theoretic environment. We study the equilibria of the game between consumers with preferences within two different dynamic pricing mechanisms, respectively the daily proportional mechanism introduced by MohsenianRad et al, and an hourly proportional mechanism. We give new results about equilibria as functions of the preference level in the case of quadratic system costs and prove that, whatever the preference level, system costs are smaller with the hourly mechanism. We simulate the Demand Response environment using real consumption data from PecanStreet database. While the Price of Anarchy remains always close to one up to 0.1% with the h
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We compare two Demand Side Management (DSM) mechanisms, introduced respectively by MohsenianRad et al (2010) and Baharlouei et al (2012), in terms of efficiency and fairness. Each mechanism defines a game where the consumers optimize their flexible consumption to reduce their electricity bills. MohsenianRad et al propose a daily mechanism for which they prove the social optimality. Baharlouei et al propose a hourly billing mechanism for which we give theoretical results: we prove the uniqueness of an equilibrium in the associated game and give an upper bound on its price of anarchy. We evaluate numerically the two mechanisms, using real consumption data from Pecan Street Inc. The simulations show that the equilibrium reached with the hourly mechanism is socially optimal up to 0.1%, and that it achieves an important fairness property according to a quantitative indicator we define. We observe that the two DSM mechanisms avoid the synchronization effect induced by non game theoretic m
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The coinvariant algebra $R_n$ is a wellstudied $\mathfrak{S}_n$module that is a graded version of the regular representation of $\mathfrak{S}_n$. Using a straightening algorithm on monomials and the GarsiaStanton basis, Adin, Brenti, and Roichman gave a description of the Frobenius image of $R_n$, graded by partitions, in terms of descents of standard Young tableaux. Motivated by the Delta Conjecture of Macdonald polynomials, Haglund, Rhoades, and Shimozono gave an extension of the coinvariant algebra $R_{n,k}$ and an extension of the GarsiaStanton basis. Chan and Rhoades further extend these results from $\mathfrak{S}_n$ to the complex reflection group $G(r,1,n)$ by defining a $G(r,1,n)$ module $S_{n,k}$ that generalizes the coinvariant algebra for $G(r,1,n)$. We extend the results of Adin, Brenti, and Roichman to $R_{n,k}$ and $S_{n,k}$.
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We consider a class of regularization methods for inverse problems where a coupled regularization is employed for the simultaneous reconstruction of data from multiple sources. Applications for such a setting can be found in multispectral or multimodality inverse problems, but also in inverse problems with dynamic data. We consider this setting in a rather general framework and derive stability and convergence results, including convergence rates. In particular, we show how parameter choice strategies adapted to the interplay of different data channels allow to improve upon convergence rates that would be obtained by merging all channels into one. Motivated by concrete applications, our results are obtained under rather general assumptions that allow to include the Kullback Leibler divergence as data discrepancy term. To simplify their application to concrete settings, we further elaborate several practically relevant special cases in detail. To complement the analytical results, we
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In this paper we discuss the relationship between the numerical range of a extensive class of unbounded operator functions and the joint numerical range of the operator coefficients. Furthermore, we derive methods on how to find estimates of the joint numerical range. Those estimates are used to obtain explicitly computable enclosures of the numerical range of the operator function and resolvent estimates. The enclosure and upper estimate of the norm of the resolvent are optimal given the estimate of the joint numerical range.
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We study local and global properties of positive solutions of ${\Delta}u=u^p]{\left {\nabla u}\right }^q$ in a domain ${\Omega}$ of ${\mathbb R}^N$, in the range $1p+q$, $p\geq 0$, $0\leq q 2$. We first prove a local Harnack inequality and nonexistence of positive solutions in ${\mathbb R}^N$ when $p(N2)+q(N1) N$ or in an exterior domain if $p(N2)+q(N1)N$ and $0\leq q1$. Using a direct Bernstein method we obtain a first range of values of $p$ and $q$ in which $u(x)\leq c({\mathrm dist\,}(x,\partial\Omega)^{\frac{q2}{p+q1}}$ This holds in particular if $p+q1+\frac{4}{n1}$. Using an integral Bernstein method we obtain a wider range of values of $p$ and $q$ in which all the global solutions are constants. Our result contains Gidas and Spruck nonexistence result as a particular case. We also study solutions under the form $u(x)=r^{\frac{q2}{p+q1}}\omega(\sigma)$. We prove existence, nonexistence and rigidity of the spherical component $\omega$ in some range of values of $N$, $p
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We introduce floating bodies for convex, not necessarily bounded subsets of $\mathbb{R}^n$. This allows us to define floating functions for convex and log concave functions and log concave measures. We establish the asymptotic behavior of the integral difference of a log concave function and its floating function. This gives rise to a new affine invariant which bears striking similarities to the Euclidean affine surface area.
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We investigate forcing and independence questions relating to construction schemes. We show that adding $\kappa\geq\omega_1$ Cohen reals adds a capturing construction scheme. We study the weaker structure of $n$capturing construction schemes and show that it is consistent to have $n$capturing construction schemes but no $(n+1)$capturing construction schemes. We also study the relation of $n$capturing with the $m$Knaster hierarchy and show that MA$_{\omega_1}($K$_m)$ and $n$capturing are independent if $n\leq m$ and incompatible if $n>m$.
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In 1953 Gale noticed that for every nperson game in extensive form with perfect information modeled by a rooted treesome special Nash equilibrium in pure strategies can be found by an algorithm of successive elimination of leaves, which is now called backward induction. He also noticed the same procedure, performed for the normal form of this game, turns into successive elimination of dominated strategies of the players that results in a single strategy profile (x_1,..., x_n), which is called a domination equilibrium (DE) and appears to be a Nashequilibrium (NE) too. In other words, the game in normal form obtained from a positional game with perfect information is dominancesolvable (DS) and also Nashsolvable (NS). Yet, an arbitrary game in normal form may be not DS. We strengthen Gale's results as follows. Consider several successive eliminations of dominated strategies that begins with X = X_1 x ... x X_n and ends in X' = X'_1 x ... x X'_n. We will call X' a Dbox of X. Our main
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The symplectic analysis for the four dimensional Pontryagin and Euler invariants is performed within the FaddeevJackiw context. The FaddeevJackiw constraints and the generalized FaddeevJackiw brackets are reported; we show that in spite of the Pontryagin and Euler classes give rise the same equations of motion, its respective symplectic structures are different to each other. In addition, a quantum state that solves the FaddeevJackiw constraints is found, and we show that the quantum states for these invariants are different to each other. Finally, we present some remarks and conclusions.
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The Generalized Lax Conjecture asks whether every hyperbolicity cone is a section of a semidefinite cone of sufficiently high dimension. We prove that the space of hyperbolicity cones of hyperbolic polynomials of degree $d$ in $n$ variables contains $(n/d)^{\Omega(d)}$ pairwise distant cones in a certain metric, and therefore that any semidefinite representation of such polynomials must have dimension at least $(n/d)^{\Omega(d)}$. The proof contains several ingredients of independent interest, including the identification of a large subspace in which the elementary symmetric polynomials lie in the relative interior of the set of hyperbolic polynomials, and quantitative versions of several basic facts about real rooted polynomials.
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We investigate whether a generic multipartite pure state can be the unique asymptotic steady state of localityconstrained purely dissipative Markovian dynamics. In the simplest tripartite setting, we show that the problem is equivalent to characterizing the solution space of a set of linear equations and establish that the set of pure states obeying the above property has either measure zero or measure one, solely depending on the subsystems' dimension. A complete analytical characterization is given when the central subsystem is a qubit. In the Npartite case, we provide conditions on the subsystems' size and the nature of the locality constraint, under which random pure states cannot be quasilocally stabilized generically. Beside allowing for the possibility to approximately stabilize entangled pure states that cannot be exact steady states in settings where stabilizability is generic, our results offer insights into the extent to which random pure states may arise as unique ground
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We consider two particles performing continuoustime nearest neighbor random walk on $\mathbb Z$ and interacting with each other when they are at neighboring positions. Typical examples are two particles in the partial exclusion process or in the inclusion process. We provide an exact formula for the LaplaceFourier transform of the transition probabilities of the twoparticle dynamics. From this we derive a general scaling limit result, which shows that the possible scaling limits are coalescing Brownian motions, reflected Brownian motions, and sticky Brownian motions. In particle systems with duality, the solution of the dynamics of two dual particles provides relevant information. We apply the exact formula to the the symmetric inclusion process, that is selfdual, in the condensation regime. We thus obtain two results. First, by computing the timedependent covariance of the particle occupation number at two lattice sites we characterize the timedependent coarsening in infinite vo
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An immense class of physical counterexamples to the four dimensional strong cosmic censor conjecturein its usual broad formulationis exhibited. More precisely, out of any closed and simply connected 4manifold an open Ricciflat Lorentzian 4manifold is constructed which is not globally hyperbolic and no perturbation of it, in any sense, can be globally hyperbolic. This very stable nonglobalhyperbolicity is the consequence of our open spaces having a "creased end" i.e., an end diffeomorphic to an exotic ${\mathbb R}^4$. Open manifolds having an end like this is a typical phenomenon in four dimensions. The construction is based on a collection of results of Gompf and Taubes on exotic and selfdual spaces, respectively, as well as applying Penrose' nonlinear graviton construction (i.e., twistor theory) to solve the Riemannian Einstein's equation. These solutions then are converted into stably nongloballyhyperbolic Lorentzian vacuum solutions. It follows that the plethora of va
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KDE.news covers the goals that the KDE project has set for itself in the coming year. "In synch with KDE's vision, Sebastian Kugler says that 'KDE is in a unique position to offer users a complete software environment that helps them to protect their privacy'. Being in that position, Sebastian explains, KDE as a FLOSS community is morally obliged to do its utmost to provide the most privacyprotecting environment for users. This is especially true since KDE has been developing not only for desktop devices, but also for mobile  an area where the respect for users' privacy is nearly nonexistent."
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So there's been a big security flaw in Apple's macOS that the company fixed in 24 hours. I rarely cover security issues because where do you draw the line, right? Anyhow, the manner of disclosure of this specific flaw is drawing some ire. Obviously, this isn't great, and the manner of disclosure didn't help much either. Usually it's advisable to disclose these vulnerabilities privately to the vendor, so that it can patch any holes before malicious parties attempt to use them for their own gains. But that ship has sailed. I've never quite understood this concept of "responsible disclosure", where you give a multibillion dollar company a few months to fix a severe security flaw before you go public. First, unless you're on that company's payroll, you have zero legal or moral responsibility to help that company protect its products or good name. Second, if the software I'm using has a severe security flaw, I'd rather very damn well please would like to know so I can do whatever I can
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One of the most popular feature requests (more than 20,000 votes) for Windows 10 is tabs in File Explorer. Microsoft has resisted adding tabs to File Explorer and apps in general for years, after originally introducing tabs in Internet Explorer 6 with a toolbar extension back in 2005. That resistance is about to change, in a big way. Microsoft is planning to add tabs to apps in Windows 10, allowing you to group together apps in a better way. Windows 10 testers will first start testing what Microsoft calls âSetsâ in the coming weeks, and the tab integration will be initially limited to Windows 10âs special Universal Windows Apps. Microsoft is planning to get as much feedback on the new feature as possible, before tweaking it and making it available to everyone. The software giant isnât committing to a specific timeline for tabs. This is an incredibly neat idea, and I can't wait to try and see if this feature makes any sense in my workflow.
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Let's have a look at the Apple Power Macintosh G5, a weighty space heater that can also perform computing tasks. Apple launched the G5 in 2003 with great fanfare, but nowadays it has a decidedly mixed legacy. In 2003 it was a desktop supercomputer that was supposed to form the basis of Apple's product range for years to come, but within three years it had been discontinued, along with the entire PowerPC range, in favour of a completely new computing architecture. The G5 puts me in mind of an ageing footballer who finally has a chance to play a World Cup match; he is called up from the substitute's bench, entertains the crowd for twenty minutes, but the team loses, and by the time of the next World Cup the uniform is the same but the players are all different. Our time in the sun is brief, the G5's time especially so. I've long been a PC person, and from my point of view the G5 came and went in the blink of an eye. I knew that it had a striking case and a reputation for high power cons
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Always after ways to push the trusty Amiga 500 to new limits, I discovered a post on the German A1k.org website about someone who had fitted a graphics card to his A500. This was a feat I felt I should replicate. I'm almost, but not quite, there. However, there were lots of hoops which needed jumping through first... It's Amiga weekend, apparently! This story is a bit more hardwarefocuseed, obviously.
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Slashdot reader overheardinpdx shares a video from the SC17 supercomputing conference where Bruce Tulloch from BitScope "describes a lowcost Rasberry Pi cluster that Los Alamos National Lab is using to simulate largescale supercomputers." Slashdot reader mspohr describes them as "five rackmount Bitscope Cluster Modules, each with 150 Raspberry Pi boards with integrated network switches." With each of the 750 chips packing four cores, it offers a 3,000core highly parallelizable platform that emulates an ARMbased supercomputer, allowing researchers to test development code without requiring a powerhungry machine at significant cost to the taxpayer. The full 750node cluster, running 23 W per processor, runs at 1000W idle, 3000W at typical and 4000W at peak (with the switches) and is substantially cheaper, if also computationally a lot slower. After development using the Pi clusters, frameworks can then be ported to the larger scale supercomputers available at Los Alamos National
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