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Last year, Freddie Gibbs, a thirtyfouryearold rapper from Gary, Indiana, was accused of dribbling a few beads of liquid tranquilizer into a young woman’s cocktail and sexually assaulting her while she was incapacitated. The event allegedly occurred in June of 2015, when Gibbs was on tour in Vienna; he was arrested a few days later, in France. Gibbs adamantly trumpeted his innocence—he refused a plea deal that would have required him to admit guilt—though, of course, these sorts of accusations alone often have instantaneous ramifications for public figures. In September of 2016, Gibbs was exonerated on all charges. “It is now selfevident he was wrongly accused,” his attorney, Theodore Simon, announced after the verdict was read. “The trial has confirmed our belief that after a searching and complete investigation and trial, the true and actual facts would be revealed—that there always was an absence of any scientific, physical, or credible evidence.”
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Bilevel optimization is defined as a mathematical program, where an optimization problem contains another optimization problem as a constraint. These problems have received significant attention from the mathematical programming community. Only limited work exists on bilevel problems using evolutionary computation techniques; however, recently there has been an increasing interest due to the proliferation of practical applications and the potential of evolutionary algorithms in tackling these problems. This paper provides a comprehensive review on bilevel optimization from the basic principles to solution strategies; both classical and evolutionary. A number of potential application problems are also discussed. To offer the readers insights on the prominent developments in the field of bilevel optimization, we have performed an automated textanalysis of an extended list of papers published on bilevel optimization to date. This paper should motivate evolutionary computation researchers
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LDPC codes are used in many applications, however, their error correcting capabilities are limited by the presence of stopping sets and trapping sets. Trapping sets and stopping sets occur when specific lowwiehgt error patterns cause a decoder to fail. Trapping sets were first discovered with investigation of the error floor of the Margulis code. Possible solutions are constructions which avoid creating trapping sets, such as progressive edge growth (PEG), or methods which remove trapping sets from existing constructions, such as graph covers. This survey examines trapping sets and stopping sets in LDPC codes over channels such as BSC, BEC and AWGNC.
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In this paper we study the reconstruction of moving object densities from undersampled dynamic Xray tomography in two dimensions. A particular motivation of this study is to use realistic measurement protocols for practical applications, i.e. we do not assume to have a full Radon transform in each time step, but only projections in few angular directions. This restriction enforces a spacetime reconstruction, which we perform by incorporating physical motion models and regularization of motion vectors in a variational framework. The methodology of optical flow, which is one of the most common methods to estimate motion between two images, is utilized to formulate a joint variational model for reconstruction and motion estimation. We provide a basic mathematical analysis of the forward model and the variational model for the image reconstruction. Moreover, we discuss the efficient numerical minimization based on alternating minimizations between images and motion vectors. A variety of
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Bargraphs are a special class of convex polyominoes. They can be identified with lattice paths with unit steps north, east, and south that start at the origin, end on the $x$axis, and stay strictly above the $x$axis everywhere except at the endpoints. Bargraphs, which are used to represent histograms and to model polymers in statistical physics, have been enumerated in the literature by semiperimeter and by several other statistics, using different methods such as the waspwaist decomposition of BousquetM\'elou and Rechnitzer, and a bijection with certain Motzkin paths. In this paper we describe an unusual bijection between bargraphs and Dyck paths, and study how some statistics are mapped by the bijection. As a consequence, we obtain a new interpretation of Catalan numbers, as counting bargraphs where the semiperimeter minus the number of peaks is fixed.
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In this paper, we consider solving a class of convex optimization problem which minimizes the sum of three convex functions $f(x)+g(x)+h(Bx)$, where $f(x)$ is differentiable with a Lipschitz continuous gradient, $g(x)$ and $h(x)$ have closedform expression of their proximity operators and $B$ is a bounded linear operator. This type of optimization problem has wide application in signal and image processing. To make full use of the differentiability function in the optimization problem, we take advantage of two operator splitting methods: the forward backward splitting method and the three operator splitting method. In the iteration scheme derived from the two operator splitting methods, we need to compute the proximity operator of $g+h \circ B$ and $h \circ B$, respectively. Although these proximity operators don't have a closedform solution, they can be solved very effectively. We mainly employ two different approaches to solving these proximity operators: one is dual and the other
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If F is a typedefinable family of commensurable subsets, subgroups or subvector spaces in a metric structure, then there is an invariant subset, subgroup or subvector space commensurable with F. This in particular applies to typedefinable or hyperdefinable objects in a classical firstorder structure.
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Apple will unveil new laptops during its annual developer conference, known as WWDC, next month, reports Bloomberg. The company is going to refresh the MacBook Pro (as well as Air and just the 'MacBook' models) with new seventhgen processors from Intel, the newest available, the report adds. Last year, Apple launched three new MacBook Pro laptops with older sixthgeneration chips, which means people who already own the newer model may be a bit dismayed by Apple's refresh. From the article: Apple is planning three new laptops, according to people familiar with the matter. The MacBook Pro will get a faster Kaby Lake processor from Intel, said the people, who requested anonymity to discuss internal planning. Apple is also working on a new version of the 12inch MacBook with a faster Intel chip. The company has also considered updating the aging 13inch MacBook Air with a new processor as sales of the laptop, Apple's cheapest, remain surprisingly strong, one of the people said.
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ArcaOS 5.0 has been released and it is available to be bought at the Arca Noae shop page. It is based on OS/2 Warp 4.52 binaries, and contains newer drivers for ACPI, USB, and networking, a new installer and several open source software projects such as Firefox, Qt, Libc, and OpenOffice. The OS2World Community also posted a statement with important OS/2 community links and some remarks on the important role open source software has in the OS/2 community.
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We formulate and prove a shape theorem for a continuoustime continuousspace stochastic growth model under certain general conditions. Similarly to the classical lattice growth models the proof makes use of the subadditive ergodic theorem. A precise expression for the speed of propagation is given in the case of a truncated free branching birth rate.
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This paper introduces the concept of atomic subspaces with respect to a bounded linear operator. Atomic subspaces generalize fusion frames and this generalization leads to the notion of $K$fusion frames. Characterizations of $K$fusion frames are discussed. Various properties of $K$fusion frames, for example, direct sums, intersection, are studied.
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It follows from the work of Burban and Drozd arXiv:0905.1231 that for nodal curves $C$, the derived category of modules over the Auslander order $\mathcal{A}_C$ provides a categorical (smooth and proper) resolution of the category of perfect complexes $\mathrm{Perf}(C)$. On the Aside, it follows from the work of HaidenKatzarkovKontsevich arXiv:1409.8611 that for punctured surfaces $X$ with stops $\Lambda$ at their boundary, the partially wrapped Fukaya category $\mathcal{W}(X,\Lambda)$ provides a categorical (smooth and proper) resolution of the compact Fukaya category $\mathcal{F}(X)$. Inspired by this analogy, we establish an equivalence between the derived category of modules over the Auslander orders over certain nodal stacky curves and partially wrapped Fukaya categories associated to punctured surfaces of arbitrary genus equipped with stops at their boundary. As an application, we deduce equivalences between perfect derived categories of coherent sheaves on such nodal stacky c
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This paper develops bootstrap methods to construct uniform confidence bands for nonparametric spectral estimation of L\'{e}vy densities under highfrequency observations. We assume that we observe $n$ discrete observations at frequency $1/\Delta > 0$, and work with the highfrequency setup where $\Delta = \Delta_{n} \to 0$ and $n\Delta \to \infty$ as $n \to \infty$. We employ a spectral (or Fourierbased) estimator of the L\'{e}vy density, and develop novel implementations of Gaussian multiplier (or wild) and empirical (or Efron's) bootstraps to construct confidence bands for the spectral estimator on a compact set that does not intersect the origin. We provide conditions under which the proposed confidence bands are asymptotically valid. Our confidence bands are shown to be asymptotically valid for a wide class of L\'{e}vy processes. We also develop a practical method for bandwidth selection, and conduct simulation studies to investigate the finite sample performance of the propose
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We improve the upper bound of the following inequalities for the gamma function $\Gamma$ due to H. Alzer and the author. \begin{equation*} \exp\left(\frac{1}{2}\psi(x+1/3)\right)<\frac{\Gamma(x)}{x^xe^{x}\sqrt{2\pi}}<\exp\left(\frac{1}{2}\psi(x)\right). \end{equation*} We also prove the following new inequalities: For $x\geq1$ \[ \sqrt{2\pi}x^xe^{x}\left(x^2+\frac{x}{3}+a_*\right)^{\frac{1}{4}}<\Gamma(x+1)<\sqrt{2\pi}x^xe^{x}\left(x^2+\frac{x}{3}+a^*\right)^{\frac{1}{4}} \] with the best possible constants $a_*=\frac{e^4}{4\pi^2}\frac{4}{3}=0.049653963176...$, and $a^*=1/18=0.055555...$, and for $x\geq0$ \begin{equation*} \exp\left[x\psi\left(\frac{x}{\log (x+1)}\right)\right]\leq\Gamma(x+1)\leq\exp\left[x\psi\left(\frac{x}{2}+1\right)\right], \end{equation*} where $\psi$ is the digamma function.
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There is renewed interest in the coideal subalgebras used to form quantum symmetric pairs because of recent discoveries showing that they play a fundamental role in the representation theory of quantized enveloping algebras. However, there is still no general theory of finitedimensional modules for these coideals. In this paper, we establish an important step in this direction: we show that every quantum symmetric pair coideal subalgebra admits a quantum Cartan subalgebra which is a polynomial ring that specializes to its classical counterpart. The construction builds on Kostant and Sugiura's classification of Cartan subalgebras for real semisimple Lie algebras via strongly orthogonal systems of positive roots. We show that these quantum Cartan subalgebras act semisimply on finitedimensional unitary modules and identify particularly nice generators of the quantum Cartan subalgebra for a family of examples.
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We extend to one dimensional quotients the result of A. Conca and S. Murai on the convexity of the regularity of Koszul cycles. By providing a relation between the regularity of Koszul cycles and Koszul homologies we prove a sharp regularity bound for the Koszul homologies of a homogeneous ideal in a polynomial ring under the same conditions.
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In this paper, we study genus $0$ equivariant relative GromovWitten invariants of $\mathbb{P}^1$ whose corresponding relative stable maps are totally ramified over one point. For fixed number of marked points, we show that such invariants are piecewise polynomials in some parameter space. The parameter space can then be divided into polynomial domains, called chambers. We determine the difference of polynomials between two neighboring chambers. In some special chamber, which we called the totally negative chamber, we show that such a polynomial can be expressed in a simple way. The chamber structure here shares some similarities to that of double Hurwitz numbers.
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In 1999 Bernasconi and Codenotti noted that the Cayley graph of a bent function is strongly regular. This paper describes the concept of extended Cayley equivalence of bent functions, discusses some connections between bent functions, designs, and codes, and explores the relationship between extended Cayley equivalence and extended affine equivalence. SageMath scripts and SageMathCloud worksheets are used to compute and display some of these relationships, for bent functions up to dimension 8.
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The moduli space $\mathcal{M}_d$ of degree $d\geq2$ rational maps can naturally be endowed with a measure $\mu_\mathrm{bif}$ detecting maximal bifurcations, called the bifurcation measure. We prove that the support of the bifurcation measure $\mu_\mathrm{bif}$ has positive Lebesgue measure. To do so, we establish a general sufficient condition for the conjugacy class of a rational map to belong to the support of $\mu_\mathrm{bif}$ and we exhibit a large set of ColletEckmann rational maps which satisfy this condition. As a consequence, we get a set of ColletEckmann rational maps of positive Lebesgue measure which are approximated by hyperbolic rational maps.
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A variety of lowdensity paritycheck (LDPC) ensembles have now been observed to approach capacity with messagepassing decoding. However, all of them use soft (i.e., nonbinary) messages and a posteriori probability (APP) decoding of their component codes. In this paper, we show that one can approach capacity at high rates using iterative harddecision decoding (HDD) of generalized product codes. Specifically, a class of spatiallycoupled GLDPC codes with BCH component codes is considered, and it is observed that, in the highrate regime, they can approach capacity under the proposed iterative HDD. These codes can be seen as generalized product codes and are closely related to braided block codes. An iterative HDD algorithm is proposed that enables one to analyze the performance of these codes via density evolution (DE).
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Hypergeometric functions and their generalizations play an important r\^{o}les in diverse applications. Many authors have been established generalizations of hypergeometric functions by a number ways. In this paper, we aim at establishing (presumably new) extended $k$type hypergeometric function $_{2}f_{1}^{k}[a, b; c; \omega; z]$ and study various properties including integral representations, differential formulas and fractional integral and derivative formula.
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An anonymous reader writes: Wall Street will be one of the first and largest industries to be automated by artificial intelligence, predicts KaiFu Lee, China's most famous venture capitalist and former Microsoft and Google executive. Lenders, money managers, and analysts  any jobs that involve crunching numbers to estimate a return  are at risk. "Banks have the curse of the baggage they have, like Kodak letting go of film," Lee says. "Their DNA is all wrong." [...] The big banks that dominate now, the venture capitalist predicts they will be outmaneuvered by smaller startups able to deploy new technology much faster.
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In this work, we propose an asymptotic preserving scheme for a nonlinear kinetic reactiontransport equation, in the regime of sharp interface. With a nonlinear reaction term of KPPtype, a phenomenon of front propagation has been proved in [9]. This behavior can be highlighted by considering a suitable hyperbolic limit of the kinetic equation, using a HopfCole transform. It has been proved in [6, 8, 11] that the logarithm of the distribution function then converges to the viscosity solution of a constrained HamiltonJacobi equation. The hyperbolic scaling and the HopfCole transform make the kinetic equation stiff. Thus, the numerical resolution of the problem is challenging, since the standard numerical methods usually lead to high computational costs in these regimes. The Asymptotic Preserving (AP) schemes have been typically introduced to deal with this difficulty, since they are designed to be stable along the transition to the macroscopic regime. The scheme we propose is adapt
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The concepts of sketching and subsampling have recently received much attention by the optimization and statistics communities. In this paper, we study NewtonSketch and Subsampled Newton (SSN) methods for the finitesum optimization problem. We consider practical versions of the two methods in which the Newton equations are solved approximately using the conjugate gradient (CG) method or a stochastic gradient iteration. We establish new complexity results for the SSNCG method that exploit the spectral properties of CG. Controlled numerical experiments compare the relative strengths of NewtonSketch and SSN methods and show that for many finitesum problems, they are far more efficient than SVRG, a popular firstorder method.
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We propose an analogue of Dubrovin's conjecture for the case where Fano manifolds have quantum connections of exponential type. It includes the case where the quantum cohomology rings are not necessarily semisimple. The conjecture is described as an isomorphism of two linear algebraic structures, which we call "mutation systems". Given such a Fano manifold $X$, one of the structures is given by the Stokes structure of the quantum connection of $X$, and the other is given by a semiorthogonal decomposition of the derived category of coherent sheaves on $X$. We also prove the conjecture for a class of smooth Fano complete intersections in a projective space.
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One of the few accepted dynamical foundations of nonadditive "nonextensive") statistical mechanics is that the choice of the appropriate entropy functional describing a system with many degrees of freedom should reflect the rate of growth of its configuration or phase space volume. We present an example of a group, as a metric space, that may be used as the phase space of a system whose ergodic behavior is statistically described by the recently proposed $\delta$entropy. This entropy is a oneparameter variation of the Boltzmann/Gibbs/Shannon functional and is quite different, in form, from the powerlaw entropies that have been recently studied. We use the first Grigorchuk group for our purposes. We comment on the connections of the above construction with the conjectured evolution of the underlying system in phase space.
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This article consists of two parts. In Part 1, we present a formulation of twodimensional topological quantum field theories in terms of a functor from a category of Ribbon graphs to the endofuntor category of a monoidal category. The key point is that the category of ribbon graphs produces all Frobenius objects. Necessary backgrounds from Frobenius algebras, topological quantum field theories, and cohomological field theories are reviewed. A result on Frobenius algebra twisted topological recursion is included at the end of Part 1. In Part 2, we explain a geometric theory of quantum curves. The focus is placed on the process of quantization as a passage from families of Hitchin spectral curves to families of opers. To make the presentation simpler, we unfold the story using SL_2(\mathbb{C})opers and rank 2 Higgs bundles defined on a compact Riemann surface $C$ of genus greater than $1$. In this case, quantum curves, opers, and projective structures in $C$ all become the same notion.
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An anonymous reader quotes a report from VentureBeat: Hewlett Packard Enterprise announced what it is calling a big breakthrough  creating a prototype of a computer with a single bank of memory that can process enormous amounts of information. The computer, known as The Machine, is a custombuilt device made for the era of big data. HPE said it has created the world's largest singlememory computer. The R&D program is the largest in the history of HPE, the former enterprise division of HP that split apart from the consumerfocused division. If the project works, it could be transformative for society. But it is no small effort, as it could require a whole new kind of software. The prototype unveiled today contains 160 terabytes (TB) of memory, capable of simultaneously working with the data held in every book in the Library of Congress five times over  or approximately 160 million books. It has never been possible to hold and manipulate whole data sets of this size in a single
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After leaving Twitter in 2011 to pursue new projects, Twitter cofounder Biz Stone has announced that he's returning to the company to "guide company culture." Stone said in a statement: "It's important that everyone understands the whole story of Twitter and each of our roles in that story. I'll shape the experience internally so it's also felt outside the company." TechCrunch reports: About a month ago Stone sold his most recent startup, Jelly, to Pinterest. He said at the time that he wasn't required to stay on with Pinterest, so was available for new opportunities. Stone said he was recently back at Twitter as a "special guest" for an event open to employees, where current CEO and fellow cofounder Jack Dorsey  another founder who left and then returned  asked him onstage if he wanted to come back and work at Twitter. After some employee cheers, and a private clarification that Jack was in fact being serious, he accepted. Twitter diehards are reacting positively to the news 
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An anonymous reader writes: If you work at Apple's One Infinite Loop headquarters in Cupertino as a computer programmer on an H1B visa, you can can be paid as little as $52,229. That's peanuts in Silicon Valley. Average wages for a programmer in Santa Clara County are more than $93,000 a year, according to the U.S. Bureau of Labor Statistics. However, the U.S. government will approve visa applications for Silicon Valley programmers at $52,229  and, in fact, did so for hundreds of potential visa holders at Apple alone. To be clear, this doesn't mean there are hundreds of programmers at Apple working for that paltry sum. Apple submitted a form to the U.S. saying it was planning on hiring 150 computer programmers beginning June 14 at this wage. But it's not doing that. Instead, this is a paperwork exercise by immigration attorneys to give an employer  in this case, Apple  maximum latitude with the H1B laws. The formssubmittal process doesn't always reflect actual hiring goals or
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“Wholly appropriate” was a phrase that H. R. McMaster, the nationalsecurity adviser, used more than half a dozen times in a press briefing on Tuesday morning, in describing what President Donald Trump revealed to Russia’s foreign minister, Sergey Lavrov, and Ambassador Sergey Kislyak in an Oval Office meeting last week. The Washington Post, followed by other media organizations, had described the conversation in a way that was wholly dismaying. The various accounts had Trump boasting about his intelligence (perhaps in both senses of the word) and showing off the most sensitive information in the same way that he showed reporters who visited his Trump Tower office the framed magazine covers on his wall, each one bearing a picture of Trump. Worse, the Post reported that the intelligence Trump bragged about came from a Middle Eastern ally that had not given permission to share it, and that might not want the Russians, in particular, to know the sources and methods by which it had learned
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For some years now, your editor has heard glowing reviews of Mosh— the "mobile shell"— as a replacement for SSH. The Mosh developers make a number of claims about its reconnection ability, performance, and security; at least some of those are relatively easily testable. After a bit of moshing, a few clear conclusions have come to the fore.
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It seems that system administrators will never shake the need for backups, even when they shove everything into the cloud. At the OpenStack Summit in Boston last week, a session by Ghanshyam Mann and Abhinav Agrawal of NEC laid out the requirements for backing up data and metadata in OpenStack—with principles that apply to any virtualization or cloud deployment.
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Yesterday afternoon, the S&P 500 closed at a record high, and is up over $1.5 trillion since the start of 2017. "And the companies doing the most to drive that rally are all tech firms," reports The Verge. "Apple, Alphabet, Facebook, Amazon, and Microsoft make up a whopping 37 percent of the total gains." From the report: All of these companies saw their share prices touch record highs in recent months. This is in stark contrast to the rest of the U.S. economy, which grew at a rate of less than 1 percent during the first three months of this year. That divide is the culmination of a longterm trend, according to a recent report featured in The Wall Street Journal: "In digital industries  technology, communications, media, software, finance and professional services  productivity grew 2.7% annually over the past 15 years...The slowdown is concentrated in physical industries  health care, transportation, education, manufacturing, retail  where productivity grew a mere 0.7% an
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Donald Trump, who may well have attempted to obstruct justice within just a few weeks of taking his oath of office, came to the Presidency with a wealth of experience in the art of deceit. He may know little of domestic or foreign policy, he may be accustomed to running an office of satraps and cronies, and he may be unable to harness an institution as complex as the executive branch, but experience told him early on that he could dodge any accusation and deny any aggression against the truth.
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Microsoft and the United Nations (UN) have announced a fiveyear "landmark" partnership to develop technology to "better predict, analyze and respond to critical human rights situations," according to a statement issued today. From a report: Additionally, Microsoft will support work being carried out by the UN Human Rights Office by contributing $5 million to a grant in what the UN called an "unprecedented level of support" from a private organization. An example of the kind of technology the duo have been working on is an information dashboard called Rights View that gives UN employees access to realtime aggregated data on rights violations by country. This, it's hoped, will "facilitate analysis, ensure early warning of emerging critical issues, and provide data to guide responses," according to Microsoft.
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An anonymous reader quotes a report from The Guardian: Infertile mice have given birth to healthy pups after having their fertility restored with ovary implants made with a 3D printer. Researchers created the synthetic ovaries by printing porous scaffolds from a gelatin ink and filling them with follicles, the tiny, fluidholding sacs that contain immature egg cells. In tests on mice that had one ovary surgically removed, scientists found that the implants hooked up to the blood supply within a week and went on to release eggs naturally through the pores built into the gelatin structures. The work marks a step towards making artificial ovaries for young women whose reproductive systems have been damaged by cancer treatments, leaving them infertile or with hormone imbalances that require them to take regular hormoneboosting drugs. Of seven mice that mated after receiving the artificial ovaries, three gave birth to pups that had developed from eggs released by the implants. The mice fed
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