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In this paper, we prove the Hamilton differential Harnack inequality for positive solutions to the heat equation of the Witten Laplacian on complete Riemannian manifolds with $CD(K, m)$condition, $m\in [n, \infty)$ and $K\geq 0$. Moreover, we introduce the $W$entropy and prove the $W$entropy formula for the fundamental solution of the Witten Laplacian on complete Riemannian manifolds with the $CD(K, m)$condition and on compact manifolds equipped with $(K, m)$super Ricci flows.
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A Hamiltonian formulation of generic manybody systems with balanced loss and gain is presented. It is shown that a Hamiltonian formulation is possible only if the balancing of loss and gain terms occur in a pairwise fashion. It is also shown that with the choice of a suitable coordinate, the Hamiltonian can always be reformulated in the background of a pseudo Euclidean metric. If the equations of motion of some of the wellknown manybody systems like Calogero models are generalized to include balanced loss and gain, it appears that the same may not be amenable to a Hamiltonian formulation. A few exactly solvable systems with balanced loss and gain, along with a set of integrals of motion is constructed. The examples include a coupled chain of nonlinear oscillators and a manyparticle Calogerotype model with fourbody inverse square plus twobody pairwise harmonic interactions. For the case of nonlinear oscillators, stable solution exists even if the dissipation parameter has unbo
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We consider random walks $\lambda$biased towards the root on a GaltonWatson tree, whose offspring distribution $(p_k)_{k\geq 1}$ is nondegenerate and has finite mean $m>1$. In the transient regime $0<\lambda <m$, the looperased trajectory of the biased random walk defines the $\lambda$harmonic ray, whose law is the $\lambda$harmonic measure on the boundary of the GaltonWatson tree. We answer a question of Lyons, Pemantle and Peres \cite{LPP97} by showing that the $\lambda$harmonic measure has a.s. strictly larger Hausdorff dimension than that of the visibility measure. We also prove that the average number of children of the vertices visited by the $\lambda$harmonic ray is a.s. bounded below by $m$ and bounded above by $m^{1}\sum k^2 p_k$. Moreover, the average number of children along the $\lambda$harmonic ray is a.s. strictly larger than the average number of children along the $\lambda$biased random walk trajectory. We observe that the latter is not monotone in
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The primary aim of this article is to extend certain inequalities concerning the preSchwarzian derivatives from the case of analytic univalent functions to that of univalent harmonic mappings defined on certain domains. This is done in two different ways. One of the ways is to connect with a conjecture on the univalent harmonic mappings. Also, we improve certain known results on the majorization of the Jacobian of functions in the affine and linear invariant family of sensepreserving harmonic mappings. This is achieved as an application of a corresponding distortion theorem in terms of the harmonic preSchwarzian derivative.
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A problem of determining zeroes of the Gauss hypergeometric function goes back to Klein, Hurwitz, and Van Vleck. In this very short note we show how ratios of hypergeometric functions arise as mfunctions of Jacobi matrices and we then revisit the problem based on the recent developments of the spectral theory of nonHermitian Jacobi matrices.
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We construct higher categories of iterated spans, possibly equipped with extra structure in the form of "local systems", and classify their fully dualizable objects. By the Cobordism Hypothesis, these give rise to framed topological quantum field theories, which are the framed versions of the "classical" TQFTs considered in the quantization programme of FreedHopkinsLurieTeleman. Using this machinery, we also construct an infinitycategory of Lagrangian correspondences between symplectic derived algebraic stacks and show that all its objects are fully dualizable.
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Given a nonconvex optimization problem, we study conditions under which every KarushKuhnTucker (KKT) point is a global optimizer. This property is known as KTinvexity and allows to identify the subset of problems where an interior point method always converges to a global optimizer. In this work, we provide necessary conditions for KTinvexity in ndimensions and show that these conditions become sufficient in the twodimensional case. As an application of our results, we study the Optimal Power Flow problem, showing that under mild assumptions on the variable's bounds, our new necessary and sufficient conditions are met for problems with two degrees of freedom.
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Despite large incentives, correctness in software remains an elusive goal. Declarative programming techniques, where algorithms are derived from a specification of the desired behavior, offer hope to address this problem, since there is a combinatorial reduction in complexity in programming in terms of specifications instead of algorithms, and arbitrary desired properties can be expressed and enforced in specifications directly. However, limitations on performance have prevented programming with declarative specifications from becoming a mainstream technique for generalpurpose programming. To address the performance bottleneck in deriving an algorithm from a specification, I propose informationgain computation, a framework where an adaptive evaluation strategy is used to efficiently perform a search which derives algorithms that provide information about a query most directly. Within this framework, opportunities to compress the search space present themselves, which suggest that inf
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We classify the threedimensional representations of the modular group that are reducible but indecomposable, and their associated spaces of holomorphic vectorvalued modular forms. We then demonstrate how such representations may be employed to compute periods of modular curves. This technique obviates the use of Hecke operators, and therefore provides a method for studying noncongruence modular curves as well as congruence.
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This paper studies the heat equation $u_t=\Delta u$ in a bounded domain $\Omega\subset\mathbb{R}^{n}(n\geq 2)$ with positive initial data and a local nonlinear Neumann boundary condition: the normal derivative $\partial u/\partial n=u^{q}$ on partial boundary $\Gamma_1\subseteq \partial\Omega$ for some $q>1$, while $\partial u/\partial n=0$ on the other part. We investigate the lower bound of the blowup time $T^{*}$ of $u$ in several aspects. First, $T^{*}$ is proved to be at least of order $(q1)^{1}$ as $q\rightarrow 1^{+}$. Since the existing upper bound is of order $(q1)^{1}$, this result is sharp. Secondly, if $\Omega$ is convex and $\Gamma_{1}$ denotes the surface area of $\Gamma_{1}$, then $T^{*}$ is shown to be at least of order $\Gamma_{1}^{\frac{1}{n1}}$ for $n\geq 3$ and $\Gamma_{1}^{1}\big/\ln\big(\Gamma_{1}^{1}\big)$ for $n=2$ as $\Gamma_{1}\rightarrow 0$, while the previous result is $\Gamma_{1}^{\alpha}$ for any $\alpha<\frac{1}{n1}$. Finally,
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In a UserPrivate Information Retrieval (UPIR) scheme, a set of users collaborate to retrieve files from a database without revealing to observers which participant in the scheme requested the file. Protocols have been proposed based on pairwise balanced designs and symmetric designs. Wepropose a new class of UPIR schemes based on generalised quadrangles (GQ). We prove that while the privacy of users in the previously proposed schemes could be compromised by a single user, the new GQUPIR schemes proposed in this paper maintain privacy with high probability even when up to $O(n^{1/4  \epsilon})$ users collude, where $n$ is the total number of users in the scheme.
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China's "Transit Elevated Bus" or TEB1 made headlines last year for its futuristic design that let it straddle two lanes of traffic, allowing cars to pass under it. Now, that very bus is the focus of an investigation. According to Quartz, "police in Beijing announced that it had started an investigation into the company behind the TEB for alleged illegal fundraising." From the report: More than 30 people associated with Huaying Kailai, an online financing platform that has been selling an investment product to raise money from individual investors to develop the bus, have been held, said Beijing's Dongcheng district police bureau in a statement (link in Chinese) on microblogging site Weibo. The statement added that the police is working to recover funds from the firm, and advised TEB investors to report their complaints to local police stations. Huaying Kailai couldn't be reached for comment. The number listed on its website is invalid and a message to the email provided bounced back.
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An anonymous reader writes Budget airline VivaColombia is considering plans to remove all seats from its planes and make passengers stand. They hope the move will drive down fares by allowing them to squeeze more passengers into each flight, opening up air travel to working class Colombians and budget holidaymakers. The nofrills carrier announced last week that it is adding 50 new Airbus 320s to its fleet to capitalise on the country's growing tourist market. The new planes will have more seats and lower running costs with the first one going into service at the start of 2018. VivaColombia's founder and CEO William Shaw told the Miami Herald the airline was looking into vertical travel options. He said: "There are people out there right now researching whether you can fly standing up  we're very interested in anything that makes travel less expensive." He added: "Who cares if you don't have an inflight entertainment system for a onehour flight? Who cares that there aren't marble fl
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An anonymous reader quotes Computerworld: Ruby has had a reputation as a userfriendly language for building web applications. But its slippage in this month's RedMonk Programming Language Rankings has raised questions about where exactly the language stands among developers these days. The twiceyearly RedMonk index ranked Ruby at eighth, the lowest position ever for the language. "Swift and now Kotlin are the obvious choices for native mobile development. Go, Rust, and others are clearer modern choices for infrastructure," said RedMonk analyst Stephen O'Grady. "The web, meanwhile, where Ruby really made its mark with Rails, is now an aggressively competitive and crowded field." Although O'Grady noted that Ruby remains "tremendously popular," participants on sites such as Hacker News and Quora have increasingly questioned whether Ruby is dying. In the Redmonk rankings, Ruby peaked at fourth place in 2013, reinforcing the perception it is in decline, if a slow one.
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schwit1 quotes Futurity: The plane of our solar system is warped in the outer reaches of the Kuiper Belt, suggesting the presence of an unknown MarstoEarthmass planetary object far beyond Pluto  but much closer than Planet Nine. An unknown, unseen "planetary mass object" may lurk in the outer reaches of our solar system, according to new research on the orbits of minor planets. The object would be different from  and much closer than  the socalled Planet Nine, a planet whose existence has yet to be confirmed... "The most likely explanation for our results is that there is some unseen mass," says Kat Volk, a postdoctoral fellow at the University of Arizona's Lunar and Planetary Laboratory and lead author of the study in the Astronomical Journal. "According to our calculations, something as massive as Mars would be needed to cause the warp that we measured."
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Longtime Slashdot reader walterbyrd shared an article from the BBC: The most extensive study to date on neonicotinoid pesticides concludes that they harm both honeybees and wild bees. Researchers said that exposure to the chemicals left honeybee hives less likely to survive over winter, while bumblebees and solitary bees produced fewer queens. The study spanned 2,000 hectares across the UK, Germany and Hungary and was set up to establish the "realworld" impacts of the pesticides... A growing number of studies have found evidence of a link between neonicotinoids and problems for bees... Data from this study has now been submitted to the European Food Standards Agency. EFSA's report on neonicotinoids in 2013 sparked Europe's temporary ban, and it is now preparing another comprehensive assessment to be released in November. The BBC adds that "Bayer, a major producer of neonicotinoids which partfunded this study, said the findings were inconclusive and that it remained convinced the p
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An anonymous reader quotes VentureBeat: GitHub wants to help more people become open source contributors with a new initiative called Open Source Friday. As the name implies, the program encourages companies to set aside time at the end of the week for their employees to work on open source projects. It's designed to bolster the ranks of open source contributors at a time when many businesses rely on freely available projects for missioncritical applications. Open Source Friday isn't just about getting businesses to offer their employees' time as a form of charity, it's also a way to improve key business infrastructure, according to Mike McQuaid, a senior software engineer at GitHub... McQuaid hopes that carving out employees' time on Fridays could help provide additional structure and incentive to participate in the ecosystem... Users don't need to be engineers in order to take part, either. While code contribution is important to the success of a project, creating and maintaining do
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Longtime Slashdot reader Paul Fernhout writes: R. Stanley Williams, of Hewlett Packard Labs, wrote a report exploring the end of Moore's Law, saying it "could be the best thing that has happened in computing since the beginning of Moore's law. Confronting the end of an epoch should enable a new era of creativity by encouraging computer scientists to invent biologically inspired devices, circuits, and architectures implemented using recently emerging technologies." This idea is also looked at in a broader shorter article by Curt Hopkins also with HP Labs. Williams argues that "The effort to scale silicon CMOS overwhelmingly dominated the intellectual and financial capital investments of industry, government, and academia, starving investigations across broad segments of computer science and locking in one dominant model for computers, the von Neumann architecture." And Hopkins points to three alternatives already being developed at Hewlett Packard Enterprise  neuromorphic computin
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"On 14 days during March, Arizona utilities got a gift from California: free solar power," reported the Los Angeles Times. Mic reports: California is generating so much solar energy that it is resorting to paying other states to take the excess electricity in order to prevent overloading power lines. According to the Los Angeles Times, Arizona residents have already saved millions in 2017 thanks to California's contribution. The state, which produced little to no solar energy just 15 years ago, has made strides  it singlehandedly has nearly half of the country's solar electricity generating capacity... When there's too much solar energy, there is a risk of the electricity grid overloading. This can result in blackouts. In times like this, California offers other states a financial incentive to take their power. But it's not as environmentally friendly as one would think. Take Arizona, for example. The state opts to put a pin in its own solar energy sources instead of fossil fuel po
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DogDude shares an article from CBS News: The science division of the White House's Office of Science and Technology Policy was unstaffed as of Friday as the three remaining employees departed this week, sources tell CBS News... On Friday afternoon, Eleanor Celeste, the assistant director for biomedical and forensic sciences at the OSTP, tweeted, "Science division out. Mic drop" before leaving the office for the last time... Under Mr. Obama, the science division was staffed with nine employees who led the charge on policy issues such as STEM education, biotechnology and crisis response. It's possible that the White House will handle these issues through staff in other divisions within the OSTP.
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In light of yesterday's post, here's a short look at the early days of Ethernet. Nowadays, we take Ethernet for granted. We plug a cable jack into the wall or a switch and we get the network. What's to think about? It didn't start that way. In the 1960s and 1970s, networks were ad hoc hodgepodges of technologies with little rhyme and less reason. But then Robert "Bob" Metcalfe was asked to create a localarea network (LAN) for Xerox's Palo Alto Research Center (PARC). His creation, Ethernet, changed everything. On a related note, in one of the recent Xerox Alto restoration videos, two of the people who worked on the invention of Ethernet, Dave Boggs and Ron Crane, helped out fixing the Alto Ethernet card  carrying some very oldfashioned Ethernet equipment and telling some great stories from the early '70s. Sadly, Ron Crane passed away 19 June.
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Thursday Lproven (Slashdot reader #6030) wrote: It appears that Ubuntu is using a feature it has added  intended to insert headlines of breaking tech news (security alerts and so on) into the Message of the Day displayed at login to the console  to display advertising and promotional messages. The message in question linked to a Hacker Noon article titled "How HBO's Silicon Valley built 'Not Hotdog' with mobile TensorFlow, Keras & React Native." Later that day Dustin Kirkland, a Ubuntu Product Manager for the feature's design (and the Core Developer for its implementation) suggested the message had been mistaken for an ad, describing it on Hacker News as a "fun fact... an interesting tidbit of potpourri from the world of Ubuntu," and later saying it was intended like Google's doodles. "Last week's message actually announced an Ubuntu conference in Latin America. The week before, we linked to an article asking for feedback on Kubuntu. Before that, we announced the availability
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An anonymous reader quotes Newsweek's latest story about fidget spinners: In a development that now seems like it was inevitable, the threepronged toys are starting to catch on fire. Gizmodo on Thursday pointed to two recent instances of Bluetoothenabled fidget spinners going up in flames while they were charging. In Alabama, a fidget spinner owned by the son of Gardendale woman Kimberly Allums caught fire after being plugged in for less than 45 minutes. In Fenton, Michigan, Michelle Carr said her spinner started smoking after charging for less than half an hour. "He noticed that it burst into flames and he just started screaming," said Allums of her son and his spinner. "I was downstairs and all I heard was 'fire...fire,' and the fidget spinner had literally, It wasn't smoking, It was in flames"... The fidget spinners in question were Bluetoothenabled so that they could light up and play music as they spun. Friday CNET ran a column titled "Fidget spinners exploding? Of course th
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An anonymous reader quotes the Seattle Times: At an exclusive gathering at a golf resort near Lisbon, the big minds of monetary policy were seriously discussing the risk that artificial intelligence could eliminate jobs on a scale that would dwarf previous waves of technological change. "There is no question we are in an era of people asking, 'Is the Robocalpyse upon us?'" David Autor, a professor of economics at the Massachusetts Institute of Technology, told an audience Tuesday that included Mario Draghi, the president of the European Central Bank, James Bullard, president of the Federal Reserve Bank of St. Louis, and dozens of other top central bankers and economists... [A]long with the optimism is a fear that the economic expansion might bypass large swaths of the population, in part because a growing number of jobs could be replaced by computers capable of learning  artificial intelligence. Policymakers and economists conceded that they have not paid enough attention to how muc
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Longtime Slashdot reader Giant Robot writes: Google Brain's latest experiment is a neural network that allows you to collaboratively draw with it inside of your web browser in realtime. The neural network is trained using the drawings collected from an earlier web game called Quick, Draw! released a few months earlier. "Once you stop doodling, the neural network takes over and attempts to guess the rest of your doodle," explains Google's page about the project, adding "You can take over drawing again and continue where you left off."
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AMD has reportedly gained 10.4 percentage points of CPU market share in the second quarter of 2017. This makes it the largest x86 CPU market share gain in the history of the Sunnyvale, California based chip maker against its much larger rival Intel. The data is courtesy of PassMark's quarterly market share report, which is based on the thousands of submissions that go through the database in any given quarter. It's important to note that because PassMark's market share data is based on benchmark submissions it counts actual systems in use, rather than systems sold. It also does not include consoles or any computer systems running operating systems other than Windows. With AMD's Ryzen processors being the new hotness right now, I'd indeed expect benchmarking sites to get more Ryzen submissions, even if it's not a 10% market share swing in favour of AMD. That being said, it's clear that AMD is having an impact right now, and as consumers, we should welcome this. I do dislike the fact
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An anonymous reader quotes Neowin's report on the newest browserusage figures from NetMarketShare: Microsoft Edge only commands a market share of 5.65%  which is an increase of only 0.02 percentage points compared to last month... it only grew by 0.56% yearoveryear. On the other hand, Google Chrome has continued its dominance with a market share of 59.49%. As a point of reference, this is a sizeable growth of 10.84 percentage points yearoveryear... Data from another firm, StatCounter, depicts an even more depressing situation for Microsoft. According to the report, Edge sits at 3.89%... Chrome is the king of all browsers according to these statistics as well, with a market share of 63.21%  a decrease of 0.14 percentage points compared to last month. Firefox, Internet Explorer, and Safari command 14%, 9.28%, and 5.16% respectively. The firm also calculates that when it comes to desktop operating systems, Windows has 91.51% of all users, followed by MacOS at 6.12 and Linux at
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