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In this paper, we study energy-efficient resource allocation in distributed antenna system (DAS) with wireless power transfer, where time-division multiple access (TDMA) is adopted for downlink multiuser information transmission. In particular, when a user is scheduled to receive information, other users harvest energy at the same time using the same radio-frequency (RF) signal. We consider two types of energy efficiency (EE) metrics: user-centric EE (UC-EE) and network-centric EE (NC-EE). Our goal is to maximize the UC-EE and NC-EE, respectively, by optimizing the transmission time and power subject to the energy harvesting requirements of the users. For both UC-EE and NC-EE maximization problems, we transform the nonconvex problems into equivalently tractable problems by using suitable mathematical tools and then develop iterative algorithms to find the globally optimal solutions. Simulation results demonstrate the superiority of the proposed methods compared with the benchmark schem
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We study the problem of minimizing the energy function $M^p(m,n) := \min \sum_{1\le i<j\le m} |\langle v_i, v_j\rangle|^p$, where $v_i$ are unit vectors in $F^n$, $F=\mathbb R$ or $\mathbb C$, $m,n,p>0$ are integers and $p$ is even. This problem has implications on finding nice polyhedra in projective spaces, and on quantum random access codes. We conduct experimental search in the complex case which suggests nice patterns on the minimum values. In some cases($p=2$ and partially $n=2$) we supply analytical proofs and give full descriptions of the minimal configurations. We also show that as $m\to \infty$, nearly equidistributed configurations points nearly give the minimal values we expect from our patterns.
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In this work we combing models of disease dynamics and economic production, and we show the potential implications of this for demonstrating the importance of savings for buffering an economy during the period of an epidemic. Finding an explicit function that relates poverty and the production of a community is an almost impossible task because of the number of variables and parameters that should be taken into account. However, studying the dynamics of an endemic disease in a region that affects its population, and therefore its ability to work, is an honest approach to understanding this function. We propose a model, perhaps the simplest, that couples two dynamics, the dynamics of an endemic disease and the dynamics of a closed economy of products and goods that the community produces in the epidemic period. Some of the results of this study are expected and known in the literature but some others are not. We highlight three of them: the interdependence that exists between health and
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We introduce the extension groups between atoms in an abelian category. For a locally noetherian Grothendieck category, the localizing subcategories closed under injective envelopes are characterized in terms of those extension groups. We also introduce the virtual dual of the extension groups between atoms to measure the global dimension of the category. A new topological property of atom spectra is revealed and it is used to relate the projective dimensions of atoms with the Krull-Gabriel dimensions. As a byproduct of the topological observation, we show that there exists a spectral space that is not homeomorphic to the atom spectrum of any abelian category.
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We give a qualitative description of extremals for the simplest version of Morrey's inequality. Our theory is based on exploiting the invariances of this inequality, studying the equation satisfied by extremals and the observation that extremals are optimal for a related convex minimization problem.
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We study the problem of decomposing a non-negative polynomial as an exact sum of squares (SOS) in the case where the associated semidefinite program is feasible but not strictly feasible (for example if the polynomial has real zeros). Computing symbolically roots of the original polynomial and applying facial reduction techniques, we can solve the problem algebraically or restrict to a subspace where the problem becomes strictly feasible and a numerical approximation can be rounded to an exact solution. As an application, we study the problem of determining when can a rational polynomial that is a sum of squares of polynomials with real coefficients be written as sum of squares of polynomials with rational coefficients, and answer this question for some previously unknown cases. We first prove that if $f$ is the sum of two squares with coefficients in an algebraic extension of ${\mathbb Q}$ of odd degree, then it can always be decomposed as a rational SOS. For the case of more than two
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Following the work of Altmann and Hausen we give a combinatorial description in terms for smooth Fano threefolds admitting a 2-torus action. We show that a whole variety of properties and invariants can be read off from this description. As an application we prove and disprove the existence of Kahler-Einstein metrics for some of these Fano threefolds, calculate their Cox rings and some of their toric canonical degenerations.
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Persistent homology is a popular data analysis technique that is used to capture the changing topology of a filtration associated with some simplicial complex $K$. These topological changes are summarized in persistence diagrams. We propose two contraction operators which when applied to $K$ and its associated filtration, bound the perturbation in the persistence diagrams. The first assumes that the underlying space of $K$ is a $2$-manifold and ensures that simplices are paired with the same simplices in the contracted complex as they are in the original. The second is for arbitrary $d$-complexes, and bounds the bottleneck distance between the initial and contracted $p$-dimensional persistence diagrams. This is accomplished by defining interleaving maps between persistence modules which arise from chain maps defined over the filtrations. In addition, we show how the second operator can efficiently compose across multiple contractions. We conclude with experiments demonstrating the seco
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Let $\Gamma_{w}$ be a non-cofinite Hecke triangle group with cusp width $w>2$ and let $\varrho\colon\Gamma_w\to U(V)$ be a finite-dimensional unitary representation of $\Gamma_w$. In this note we announce a new fractal upper bound for the Selberg zeta function of $\Gamma_{w}$ twisted by $\varrho$. In strips parallel to the imaginary axis and bounded away from the real axis, the Selberg zeta function is bounded by $\exp\left( C_{\varepsilon} \vert s\vert^{\delta + \varepsilon} \right)$, where $\delta = \delta_{w}$ denotes the Hausdorff dimension of the limit set of $\Gamma_{w}$. This bound implies fractal Weyl bounds on the resonances of the Laplacian for all geometrically finite surfaces $X=\widetilde{\Gamma}\backslash\mathbb{H}$ where $\widetilde{\Gamma}$ is a finite index, torsion-free subgroup of $\Gamma_w$.
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We establish a functional limit theorem for joint laws of occupation time processes of infinite ergodic transformations, in the sense of strong distributional convergence. Our limit theorem is a functional and joint-distributional extention both of Aaronson's limit theorem of Darling--Kac type, and of Thaler's generalized arcsine laws of Lamperti type, at the same time. We apply it to obtain a functional limit theorem for joint laws of sojourns of interval maps near and away from indifferent fixed points. For the proof, we represent occupation times in terms of excursion lengths, and show a functional convergence of excursion lengths to stable L\'evy processes.
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We consider the deformation theory of two kinds of geometric objects: foliations on one hand, pre-symplectic forms on the other. For each of them, we prove that the geometric notion of equivalence given by isotopies agrees with the algebraic notion of gauge equivalence obtained from the $L_{\infty}$-algebras governing these deformation problems.
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In this note we construct a "restriction" map from the cocenter of a reductive group G over a local non-archimedean field F to the cocenter of a Levi subgroup. We show that the dual map corresponds to parabolic induction and deduce that parabolic induction preserves stability. We also give a new (purely geometric) proof that the character of normalized parabolic induction does not depend on a parabolic subgroup. In the appendix, we use a similar argument to extend a theorem of Lusztig-Spaltenstein on induced unipotent classes to all infinite fields.
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In this review paper I present two geometric constructions of distinguished nature, one is over the field of complex numbers $\mathbb{C}$ and the other one is over the two elements field $\mathbb{F}_2$. Both constructions have been employed in the past fifteen years to describe two quantum paradoxes or two resources of quantum information: entanglement of pure multipartite systems on one side and contextuality on the other. Both geometric constructions are linked to representation of semi-simple Lie groups/algebras. To emphasize this aspect one explains on one hand how well-known results in representation theory allows one to see all the classification of entanglement classes of various tripartite quantum systems ($3$ qubits, $3$ fermions, $3$ bosonic qubits...) in a unified picture. On the other hand, one also shows how some weight diagrams of simple Lie groups are encapsulated in the geometry which deals with the commutation relations of the generalized $N$-Pauli group.
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In this paper, we establish global $C^{1+\alpha,\frac{1+\alpha}{2}}$ estimates for solutions of the linearized parabolic Monge-Amp$\grave{e}$re equation $$\mathcal{L}_\phi u(x,t):=-u_t\,\mathrm{det}D^2\phi(x)+\mathrm{tr}[\Phi(x) D^2 u]=f(x,t)$$ under appropriate conditions on the domain, Monge-Amp$\grave{e}$re measures, boundary data and $f$, where $\Phi:=\mathrm{det}(D^2\phi)(D^2\phi)^{-1}$ is the cofactor of the Hessian of $D^2\phi$.
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In this paper, we establish global $W^{2,p}$ estimates for solutions of the linearized Monge-Amp$\grave{e}$re equation $$\mathcal{L}_{\phi}u:=\mathrm{tr}[\Phi D^2 u]=f,$$ where the density of the Monge-Amp$\grave{e}$re measure $g:=\mathrm{det}D^2\phi$ satisfies a $\mathrm{VMO}$-type condition, and $\Phi:=(\mathrm{det}D^2\phi)(D^2\phi)^{-1}$ is the cofactor matrix of $D^2\phi$.
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We study the connection between the Baum-Connes conjecture for an ample groupoid $G$ with coefficient $A$ and the K\"unneth formula for the K-theory of tensor products by the crossed product $A\rtimes_r G$. To do so we develop the machinery of Going-Down functors for ample groupoids. As an application we prove that both the uniform Roe algebra of a coarse space which uniformly embeds into a Hilbert space and the maximal Roe algebra of a space admitting a fibred coarse embedding into a Hilbert space satisfy the K\"unneth formula. We also provide a stability result for the K\"unneth formula using controlled K-theory, and apply it to give an example of a space that does not admit a coarse embedding into a Hilbert space, but whose uniform Roe algebra satisfies the K\"unneth formula. As a by-product of our methods, we also prove a permanence property for the Baum-Connes conjecture with respect to equivariant inductive limits of the coefficient algebra.
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We consider the discrete, fractional operator $\left(L_a^\nu x\right) (t) := \nabla [p(t) \nabla_{a^*}^\nu x(t)] + q(t) x(t-1)$ involving the nabla Caputo fractional difference, which can be thought of as an analogue to the self-adjoint differential operator. We show that solutions to difference equations involving this operator have expected properties, such as the form of solutions to homogeneous and nonhomogeneous equations. We also give a variation of constants formula via a Cauchy function in order to solve initial value problems involving $L_a^\nu$. We also consider boundary value problems of any fractional order involving $L_a^\nu$. We solve these BVPs by giving a definition of a Green's function along with a corresponding Green's Theorem. Finally, we consider a (2,1) conjugate BVP as a special case of the more general Green's function definition.
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Hereditarily non uniformly perfect (HNUP) sets were introduced by Stankewitz, Sugawa, and Sumi in \cite{SSS} who gave several examples of such sets based on Cantor set-like constructions using nested intervals. We exhibit a class of examples in non-autonomous iteration where one considers compositions of polynomials from a sequence which is in general allowed to vary. In particular, we give a sharp criterion for when Julia sets from our class will be HNUP and we show that the maximum possible Hausdorff dimension of $1$ for these Julia sets can be attained. The proof of the latter considers the Julia set as the limit set of a non-autonomous conformal iterated function system and we calculate the Hausdorff dimension using a version of Bowen's formula given in the paper by Rempe-Gillen and Urb\'{a}nski \cite{RU}
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Gallagher's theorem is a sharpening and extension of the Littlewood conjecture that holds for almost all tuples of real numbers. We provide a fibre refinement, solving a problem posed by Beresnevich, Haynes and Velani in 2015. Hitherto, this was only known on the plane, as previous approaches relied heavily on the theory of continued fractions. Using reduced successive minima in lieu of continued fractions, we develop the structural theory of Bohr sets of arbitrary rank, in the context of diophantine approximation. In addition, we generalise the theory and result to the inhomogeneous setting. To deal with this inhomogeneity, we employ diophantine transference inequalities in lieu of the three distance theorem.
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We exhibit three double octic Calabi--Yau threefolds over the certain quadratic fields and prove their modularity. The non-rigid threefold has two conjugate Hilbert modular forms of weight [4,2] and [2,4] attached while the two rigid threefolds correspond to a Hilbert modular form of weight [4,4] and to the twist of the restriction of a classical modular form of weight 4.
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It is noted that using complex Hessian equations and the concavity inequalities for elementary symmetric polynomials implies a generalized form of Hodge index inequality. Inspired by this result, using G{\aa}rding's theory for hyperbolic polynomials, we obtain a mixed Hodge-index type theorem for classes of type $(1,1)$. The new feature is that this Hodge-index type theorem holds with respect to mixed polarizations in which some satisfy particular positivity condition, but could be degenerate and even negative along some directions.
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We consider geothermal inverse problems and uncertainty quantification from a Bayesian perspective. Our goal is to make standard, 'out-of-the-box' Markov chain Monte Carlo (MCMC) sampling more feasible for complex simulation models. To do this, we first show how to pose the inverse and prediction problems in a hierarchical Bayesian framework. We then show how to incorporate so-called posterior model approximation error into this hierarchical framework, using a modified form of the Bayesian approximation error (BAE) approach. This enables the use of a 'coarse', approximate model in place of a finer, more expensive model, while also accounting for the additional uncertainty and potential bias that this can introduce. Our method requires only simple probability modelling and only modifies the target posterior - the same standard MCMC sampling algorithm can be used to sample the new target posterior. We show that our approach can achieve significant computational speed-ups on a geothermal
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For a Tychonoff space $X$ and a family $\lambda$ of subsets of $X$, we denote by $C_{\lambda}(X)$ the $T_1$-space of all real-valued continuous functions on $X$ with the $\lambda$ -open topology. A topological space is productively Lindel\"of if its product with every Lindel\"of space is Lindel\"of. A space is indestructibly productively Lindel\"of if it is productively Lindel\"of in any extension by countably closed forcing. In this paper, we study indestructibly productively Lindel\"of and Menger function space $C_{\lambda}(X)$.
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Simple inequalities are established for integrals of the type $\int_0^x \mathrm{e}^{-\gamma t} t^{-\nu} \mathbf{L}_\nu(t)\,\mathrm{d}t$, where $x>0$, $0\leq\gamma<1$, $\nu>-\frac{3}{2}$ and $\mathbf{L}_{\nu}(x)$ is the modified Struve function of the first kind. In most cases, these inequalities are tight in certain limits. As a consequence we deduce a tight double inequality, involving the modified Struve function $\mathbf{L}_{\nu}(x)$, for a generalized hypergeometric function.
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We prove the instability of some families of Riemannian manifolds with non-trivial real Killing spinors. These include the invariant Einstein metrics on the Aloff-Wallach spaces $N_{k, l}={\rm SU}(3)/i_{k, l}(S^{1})$ (which are all nearly ${\rm G}_2$ except $N_{1,0}$), and Sasaki Einstein circle bundles over certain irreducible Hermitian symmetric spaces. We also prove the instability of most of the simply connected non-symmetric compact homogeneous Einstein spaces of dimensions $5, 6, $ and $7$, including the strict nearly K\"ahler ones (except ${\rm G}_2/{\rm SU}(3)$).
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In this paper, we establish interior $C^{1,\alpha}$ estimates for solutions of the linearized Monge-Amp$\grave{e}$re equation $$\mathcal{L}_{\phi}u:=\mathrm{tr}[\Phi D^2 u]=f,$$ where the density of the Monge-Amp$\grave{e}$re measure $g:=\mathrm{det}D^2\phi$ satisfies a $\mathrm{VMO}$-type condition and $\Phi:=(\mathrm{det}D^2\phi)(D^2\phi)^{-1}$ is the cofactor matrix of $D^2\phi$.
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Novel reconstruction methods for electrical impedance tomography (EIT) often require voltage measurements on current-driven electrodes. Such measurements are notoriously difficult to obtain in practice as they tend to be affected by unknown contact impedances and require problematic simultaneous measurements of voltage and current. In this work, we develop an interpolation method that predicts the voltages on current-driven electrodes from the more reliable measurements on current-free electrodes for difference EIT settings, where a conductivity change is to be recovered from difference measurements. Our new method requires the a-priori knowledge of an upper bound of the conductivity change, and utilizes this bound to interpolate in a way that is consistent with the special geometry-specific smoothness of difference EIT data. Our new interpolation method is computationally cheap enough to allow for real-time applications, and simple to implement as it can be formulated with the standar
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An anonymous reader writes: The Kaiser Family Foundation's annual review of employer-based insurance shows that 21% of large employers collect health information from employees' mobile apps or wearable devices, as part of their wellness programs -- up from 14% last year. Wellness programs are voluntary, and so is contributing your health information to them. But among companies that offer a wellness program, just 9% of employers (including 35% of large employers) offer workers an incentive to participate.
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Nadav Amit decided to dig into why some small kernel functions were not being inlined by GCC; the result is a detailed investigation into how these things can go wrong. "Ignoring the assembly shenanigans that this code uses, we can see that in practice it generates a single ud2 instruction. However, the compiler considers this code to be 'big' and consequently oftentimes does not inline functions that use WARN() or similar functions. The reason turns to be the newline characters (marked as '\n' above). The kernel compiler, GCC, is unaware to the code size that will be generated by the inline assembly. It therefore tries to estimate its size based on newline characters and statement separators (';' on x86)."
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Even though the Mac line has grown less repairable over time, fixers have still managed to develop techniques for performing essential screen and battery repairs - until now. According to an internal Apple service document, any Mac with an Apple T2 chip now requires the proprietary 'Apple Service Toolkit 2 (AST 2) System Configuration Suite' (whew, that's a mouthful!) to complete certain repairs. This issue has received extensive coverage, but we wanted to perform some lab testing before we took our shot. Let's break down what all this means first. This is inevitable - Macs have becoming ever more closed and less repairable for years now. This sucks - but at the same time, nobody is forcing you to buy a Mac. There are countless premium Windows and Linux laptops out there that are just as good, and even many non-premium Windows laptops are more than good enough replacements.
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tedlistens writes: Police officers wearing new cameras by Axon, the U.S.'s largest body camera supplier, will soon be able to send live video from their cameras back to base and elsewhere, potentially expanding police surveillance. Another feature of the new device -- set to be released next year -- triggers the camera to start recording and alerts command staff once an officer has fired their weapon, a possible corrective to the problem of officers forgetting to switch them on. (The initial price of $699 doesn't include other costs, like a subscription to Axon's Evidence.com data management system.) But adding new technologies to body camera video introduces new privacy concerns, say legal experts, who have cautioned that a network of live-streaming cameras risks turning officers into roving sentinels for a giant panopticon-like surveillance system. Harlan Yu, the executive director of Upturn, a Washington nonprofit consultancy that has studied body cameras, says that live-streaming c
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China has issued a new regulation setting out wide-ranging police powers to inspect internet service providers and users, as the government tightens its grip on the country's heavily restricted cyberspace. Local media reports: Under the new rule, effective from November 1, central and local public security authorities can enter the premises of all companies and entities that provide internet services and look up and copy information considered relevant to cybersecurity. The regulation was issued by the Ministry of Public Security last month and released on its website on Sunday. It comes more than a year after a controversial cybersecurity law was introduced that has caused widespread concern among foreign companies operating in China. Despite its broad scope, the legislation gives few details about implementation, making it all the more difficult for companies trying to avoid its repercussions. Analysts said the new regulation sheds some light on how the law will be implemented. "That
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Hackaday's Tom Nardi writes about the Federal Aviation Administration's push to repeal Section 336, which states that small remote-controlled aircraft as used for hobby and educational purposes aren't under FAA jurisdiction. "Despite assurances that the FAA will work towards implementing waivers for hobbyists, critics worry that in the worst case the repeal of Section 336 might mean that remote control pilots and their craft may be held to the same standards as their human-carrying counterparts," writes Nardi. From the report: Section 336 has already been used to shoot down the FAA's ill-conceived attempt to get RC pilots to register themselves and their craft, so it's little surprise they're eager to get rid of it. But they aren't alone. The Commercial Drone Alliance, a non-profit association dedicated to supporting enterprise use of Unmanned Aerial Systems (UAS), expressed their support for repealing Section 336 in a June press release: "Basic 'rules of the road' are needed to manage
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Citing corporate values, Google has decided not to compete for the Pentagon's $10 billion cloud-computing contract. Bloomberg reports: The project, known as the Joint Enterprise Defense Infrastructure cloud, or JEDI, involves transitioning massive amounts of Defense Department data to a commercially operated cloud system. Companies are due to submit bids for the contract, which could last as long as 10 years, on October 12th. Google's announcement on Monday came just months after the company decided not to renew its contract with a Pentagon artificial intelligence program, after extensive protests from employees of the internet giant about working with the military. The company then released a set of principles designed to evaluate what kind of artificial intelligence projects it would pursue. "We are not bidding on the JEDI contract because first, we couldn't be assured that it would align with our AI Principles," a Google spokesman said in a statement. "And second, we determined that
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Google exposed the private data of hundreds of thousands of users of the Google+ social network and then opted not to disclose the issue this past spring, in part because of fears that doing so would draw regulatory scrutiny and cause reputational damage, WSJ reported Monday, citing people briefed on the incident and documents. From the report: As part of its response to the incident, the Alphabet unit plans to announce a sweeping set of data privacy measures that include permanently shutting down all consumer functionality of Google+, the people said. The move effectively puts the final nail in the coffin of a product that was launched in 2011 to challenge Facebook and is widely seen as one of Google's biggest failures. A software glitch in the social site gave outside developers potential access to private Google+ profile data between 2015 and March 2018, [Editor's note: the link may be paywalled; alternative source] when internal investigators discovered and fixed the issue, accordi
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Google exposed the private data of hundreds of thousands of users of the Google+ social network and then opted not to disclose the issue this past spring, in part because of fears that doing so would draw regulatory scrutiny and cause reputational damage, according to people briefed on the incident and documents reviewed by The Wall Street Journal. [...] A software glitch in the social site gave outside developers potential access to private Google+ profile data between 2015 and March 2018, when internal investigators discovered and fixed the issue, according to the documents and people briefed on the incident. A memo reviewed by the Journal prepared by Google's legal and policy staff and shared with senior executives warned that disclosing the incident would likely trigger "immediate regulatory interest" and invite comparisons to Facebook's leak of user information to data firm Cambridge Analytica. Data leaks and breaches happen. They are a fact of life we're pretty much
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The Hubble Space Telescope is operating with only essential functions after it lost one of the gyroscopes needed to point the spacecraft. From a report: The observatory, described as one of the most important scientific instruments ever created, was placed in "safe mode" over the weekend, while scientists try to fix the problem. Hubble had been operating with four of its six gyroscopes when one of them failed on Friday. The telescope was launched in 1990. After the gyro failure at the weekend, controllers tried to switch on a different one, but that was found to be malfunctioning. That leaves Hubble with only two fully functional gyros. At any given time, Hubble needs three of its gyroscopes to work for optimal efficiency.
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An anonymous reader shares a report: Four years ago, IBM announced that it was investing $3 billion over the next five years into the future of nanoelectronics with a broad project it dubbed "7nm and Beyond." With at least one major chipmaker, GlobalFoundries, hitting the wall at the 7-nm node, IBM is forging ahead, using graphene to deposit nanomaterials in predefined locations without chemical contamination. In research described in the journal Nature Communications, the IBM researchers for the first time electrified graphene so that it helps to deposit nanomaterials with 97% accuracy. "As this method works for a wide variety of nanomaterials, we envision integrated devices with functionalities that represent the unique physical properties of the nanomaterial," said Mathias Steiner, manager at IBM Research-Brazil. "We also can envision on-chip light detectors and emitters operating within a distinct wavelength range determined by the optical properties of the nanomaterial." As an exa
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Intel unveiled its 9th-generation Core desktop chips, with the notable omission of a key feature: Hyper-Threading, at least on all but the most exclusive Core i9-9900K for mainstream PCs. Hyper-Threading has also been reserved for a new iteration of Intel's X-series processors, which includes up to 18 cores and 36 threads. From a report: In a livestream Monday morning from its Fall Launch Event in New York, the company announced just a single Core i9 chip, the $488 Core i9-9900K. Later, the company privately revealed two others in the Core i7 and Core i5 families. Intel also announced a new series of X-class chips, ranging from 8 cores and 16 threads through 18 cores and 36 threads. Prices will range from $589 to $1,979. It's certainly fair to say that Intel surprised us all with the unexpected shift of its upcoming 28-core chip to the Xeon family, as well as the announcement of the X-series chips, too. And what's the deal with hyperthreading? Intel's announcement certainly adds some n
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Among many of Intel's announcements today, a key one for a lot of users will be the launch of Intel's 9th Generation Core desktop processors, offering up to 8-cores on Intel's mainstream consumer platform. These processors are drop-in compatible with current Coffee Lake and Z370 platforms, but are accompanied by a new Z390 chipset and associated motherboards as well. The highlights from this launch is the 8-core Core i9 parts, which include a 5.0 GHz turbo Core i9-9900K, rated at a 95W TDP. Biggest news for me is that Intel unveiled that these new processors will switch from a cheap paste as thermal interface material between the die and the IHS to a layer of solder. This should greatly aid in cooling.
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An anonymous reader quotes a report from Ars Technica: Lawyers representing a Southern California limousine company that sued Uber last month over state unfair competition allegations have now filed a motion for partial summary judgement. If the filing is granted by the judge, the motion would substantially streamline the case and answer the vexing question: are Uber drivers employees or not? The proposed class-action lawsuit, known as Diva Limousine v. Uber, relies on a recently decided California Supreme Court decision that makes it more difficult for companies to unilaterally declare their workers as contractors, which effectively deprives them of benefits that they would otherwise receive as employees. In the California Supreme Court case, known as Dynamex, that court came up with a three-part test, known as the ABC test, to figure out whether companies can assert contractor status or not: "(A) that the worker is free from the control and direction of the hiring entity in connectio
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Earlier this month, The New York Times ran a story which looks at the ways a network of illegal radio stations changed British music, and wonders where young people are going to make culture now, now that the internet is killing off the pirate radio. An excerpt from the story: Ofcom, the British communications regulator, estimated there are now just 50 pirate stations in London, down from about 100 a decade ago, and hundreds in the 1990s, when stations were constantly starting up and shutting down. Ofcom considers this good news, because illegal broadcasters could interfere with radio frequencies used by emergency services and air traffic control, a spokesman said. But pirate radio stations also offered public services, of a different sort: They gave immigrant communities programming in their native languages, ran charity drives and created the first radio specifically for black Britons. Pirate radio was also the site of some of Britain's most important musical innovations, introducing
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Let $G$ be a semisimple algebraic group over a field of characteristic $p > 0$. We prove that the dual Weyl modules for $G$ all have $p$-filtrations when $p$ is not too small. Moreover, we give applications of this theorem to $p^n$-filtrations for $n > 1$, to modules containing the Steinberg module as a tensor factor, and to the Donkin conjecture on modules having $p$-filtrations.
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A graph $G$ is called edge-magic if there is a bijective function $f$ from the set of vertices and edges to the set $\{1,2,\ldots,|V(G)|+|E(G)|\}$ such that the sum $f(x)+f(xy)+f(y)$ for any $xy$ in $E(G)$ is constant. Such a function is called an edge-magic labelling of G and the constant is called the valence of $f$. An edge-magic labelling with the extra property that $f(V(G))= \{1,2,\ldots,|V(G)|\}$ is called super edge-magic. In this paper, we establish a relationship between the valences of (super) edge-magic labelings of certain types of bipartite graphs and the existence of a particular type of decompositions of such graphs.
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A convex optimization-based method is proposed to numerically solve dynamic programs in continuous state and action spaces. This approach using a discretization of the state space has the following salient features. First, by introducing an auxiliary optimization variable that assigns the contribution of each grid point, it does not require an interpolation in solving an associated Bellman equation and constructing a control policy. Second, the proposed method allows us to solve the Bellman equation with a desired level of precision via convex programming in the case of linear systems and convex costs. We can also construct a control policy of which performance converges to the optimum as the grid resolution becomes finer in this case. Third, when a nonlinear control-affine system is considered, the convex optimization approach provides an approximate control policy with a provable suboptimality bound. Fourth, for general cases, the proposed convex formulation of dynamic programming op
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First-Fit is a greedy algorithm for partitioning the elements of a poset into chains. Let $\textrm{FF}(w,Q)$ be the maximum number of chains that First-Fit uses on a $Q$-free poset of width $w$. A result due to Bosek, Krawczyk, and Matecki states that $\textrm{FF}(w,Q)$ is finite when $Q$ has width at most $2$. We describe a family of posets $\mathcal{Q}$ and show that the following dichotomy holds: if $Q\in\mathcal{Q}$, then $\textrm{FF}(w,Q) \le 2^{c(\log w)^2}$ for some constant $c$ depending only on $Q$, and if $Q\not\in\mathcal{Q}$, then $\textrm{FF}(w,Q) \ge 2^w - 1$.
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Computationally efficient numerical methods for high-order approximations of convolution integrals involving weakly singular kernels find many practical applications including those in the development of fast quadrature methods for numerical solution of integral equations. Most fast techniques in this direction utilize uniform grid discretizations of the integral that facilitate the use of FFT for $O(n\log n)$ computations on a grid of size $n$. In general, however, the resulting error converges slowly with increasing $n$ when the integrand does not have a smooth periodic extension. Such extensions, in fact, are often discontinuous and, therefore, their approximations by truncated Fourier series suffer from Gibb's oscillations. In this paper, we present and analyze an $O(n\log n)$ scheme, based on a Fourier extension approach for removing such unwanted oscillations, that not only converges with high-order but is also relatively simple to implement. We include a theoretical error analys
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We present a hybrid spectral element-Fourier spectral method for solving the coupled system of Navier-Stokes and Cahn-Hilliard equations to simulate wall-bounded two-phase flows in a three-dimensional domain which is homogeneous in at least one direction. Fourier spectral expansions are employed along the homogeneous direction and $C^0$ high-order spectral element expansions are employed in the other directions. A critical component of the method is a strategy we developed in a previous work for dealing with the variable density/viscosity of the two-phase mixture, which makes the efficient use of Fourier expansions in the current work possible for two-phase flows with different densities and viscosities for the two fluids. The attractive feature of the presented method lies in that the two-phase computations in the three-dimensional space are transformed into a set of de-coupled two-dimensional computations in the planes of the non-homogeneous directions. The overall scheme consists of
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