We're so excited to have a huge guest on the show – big time comedian and noted metalhead, Brian Posehn,...

The post METAL INJECTION LIVECAST #551 - Where Nickelback Shines with special guest Comedian Brian Posehn appeared first on Metal Injection.

What's with all the good drummers dying? We kick things off discussing the sad news. Noa discussed locking herself out...

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What an eventful edition of the Metal Injection Livecast! We kick things off talking about the new Dave Mustaine memoir...

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We kick things off talking about the Rage Against the Machine reunion. We then discuss the summer touring season and...

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Michiel Dullaert, data visualization expert and trainer from the Netherlands, has updated his Chart Guide poster to version 4! A free PDF is available for download from his website, and introduces a new category, 19 new charts and 4 extra design tips. You can also purchase a full-size printed poster version.

As the November 2019 Giveaway, I have a pair of Chart Guide posters, that will be shipped to one lucky winner. That way you get one for yourself, and one you can give to a friend or coworker.

Register HERE by November 30, 2019 at 11:59pm CT, and the winner will be randomly chosen on December 1st!

This poster shows 84 charts to choose from and includes 16 chart design tips to help you make the Perfect Chart. The poster is available as a big poster or you can download the PDF file for free. Let this ChartGuide poster help you choose and design your Perfect Chart.

You can see his complete write-up about the new version HERE. I was able to ask Michiel a few interview questions about developing the posters:

Cool Infographics: What’s your background and how did you get into visualizing data?

Michiel Dullaert: Years ago I have been working in the boardgame and puzzle industry. Part of my work was discovering new boardgames and puzzles and introduce them to the market. I was working for two different companies, both at the time that a new product of theirs really changed the market. For the boardgame industry I worked for the company that introduced a new type of boardgame (the game of Catan) that made playing boardgames a popular hobby. After that, I worked for a company that created puzzle magazines at the time the Sudoku puzzles was introduced. And here the same happened again, a new type of puzzle that changed the way people would puzzle and talk about puzzles. Both were very nice jobs, with a lot of enthusiastic conversations with customers about new products.

In both companies I was working in the product development. I always had a large personal interest in the data behind the products. So it felt logic to do more with data, and I changed careers. I started working for a large company as an analyst. And it was not long that I found out that my colleagues were not interested in my reports. Although the reports contained interesting information it was shown in large tables and busy charts. People seemed to be not interested and if the looked into the numbers, they did not seem to understand them. My work did not seem to matter. The contrast between my previous jobs and the work as an analyst could not have been bigger. At that time I decided I would try to find a way to make people as enthusiastic about data as they were about boardgames and Sudoku puzzles. 

The first step was reading books on the topic of data visualization. Because I was working in the business intelligence field, the most logic choice were the books of Stephen Few. I bought them all and a whole new world opened for me. When Few was in the Netherlands to give a course I felt very lucky I could join. The workshops inspired me to learn more on this topic. So I bought more books and the next year I joined a class of Alberto Caïro. This gave me multiple perspectives on the same topic. The things I learned were applied to my work, and I was getting more and more responses on my visualizations. People actually started to read and understand them. 

My manager asked me to explain my choices in visualizations to my colleagues, so they could learn from me. And then I discovered how great it is to teach about data visualisation. I met a couple of UX designers and they inspired me learn more about that topic and to get an UX certification. The knowledge I gained in learning UX helped me in developing my own perspective on good data visualization. And in my workshop I try to inspire others to create such. For these workshops I wanted an overview of charts. Although there were already some great overviews, none of them had the point of view I was teaching in class. So I decided to design my own. That’s how Chart.Guide started. 

Cool Infographics: Who is the Chart Guide poster intended for?

Michiel Dullaert: The website and the posters are intended for everyone who makes charts. For me it does not matter if you are working as a data-journalist or a data scientist, a infographic designer, project manager or a financial analyst. As long as you need help or inspiration when making charts or tables, Chart.Guide can help you. Online in the form of the website and offline in the form of the poster. Because I want to inspire as many people as possible I made the PDF of the poster free to download. I know that the poster is used in business departments, newsrooms and in school classrooms.

Cool Infographics: What was your design process for the poster?

Michiel Dullaert: The main source for updates to the poster or website, is the conversations I have with people I teach or work with. If they have a need for certain chart types, or make design mistakes, I try to add that topic. 

The first poster edition (picture DPG Chart Chooser) was just a collection of charts I created for my students. For each chart a few words on when to use the chart and, more important, it gave advice on what charts were not recommended. On the second edition (the first under the Chart.Guide brand) I added chart design tips.  The reason, I saw people choose a good chart but then mess up the design. Last year, I got questions about maps, so I decided to add them on poster edition 4. 

The design process starts with insight I get from conversations I am having. Next step is cutting the old poster and rearranging everything. (see picture ChartGuide rearrange) now, will lead to more insights on the poster in the future. Although it make take some time to transform everything to the screen or paper. I still need to find some time to explain on the website why some charts are “not recommended”. 

Cool Infographics: You asked your followers to help choose the design of the new poster. How did that go?

Michiel Dullaert: The poster is made to help people. So it seems to be logic to give them a role in the design process. As a UX designer I like to test my designs before releasing them. Most of these tests are done in class, because I like to observe the users in how they use the new design. The online voting was suggestion of a student. It did give me a lot of useful feedback. Especially when people wrote a lot of text explaining their choice. For future editions I will do the same.

Cool Infographics: How can people follow you for updates?

Michiel Dullaert: People who have downloaded the PDF will get an email when a new poster is available, or when something interesting is added to the website. For this and more chart related inspiration, they can follow me on Twitter: @Chart_Guide or on facebook: /ChartGuide1.

This helpful reference guide is one of over 25 FREE data visualization guides I maintain links to in the Cool Infographics Tools pages. See them all on the DataViz Reference Guides page, and let me know if I’m missing any.

By Jessica Corbett Common Dreams “The most robust study of the ice mass balance of Antarctica to date,” scientists say, “now puts Antarctica in the frame as one of the largest contributors to sea-level rise.” Scientists are expressing alarm over … Continue reading →

Successful design manages cognitive load. Cognitive load is a technical term for “mental effort,” more specifically it’s the total amount of mental effort required for a given task. Completing any task requires some level of mental effort. This includes learning new information, analyzing stimuli, and working with short and long-term memory. Mental energy which has […]

The post What is cognitive load and why does it matter in web and interface design? appeared first on Psychology of Web Design | 3.7 Blog.

If you’re not familiar with cognitive load and how it impacts interface design, it’s worth reviewing our previous blog post. If you’re already convinced cognitive load is important, the next step is addressing it. Reducing cognitive load is accomplished by reducing or offloading mental effort (which are similar but different concepts.) Reducing mental effort is […]

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You’re hiring a web designer or providing web design services, what’s included in a normal project? In other words, what are the deliverables, and the use of a membership website builder could be essential for this. Let’s start by defining what a deliverable is. Wikipedia defines a deliverable as: …a tangible or intangible good or […]

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Are you looking for the best GoDaddy alternative for domain registration and web hosting? Without a doubt, Godaddy is one of the most popular names when it comes to registering domain names and hosting your business online. Over the last 22 years, GoDaddy has managed to establish a stronghold in the market. In this article, […]

The post 12 Best GoDaddy Alternatives for Domain & Web Hosting (2020) appeared first on IsItWP - Free WordPress Theme Detector.

Adam offers advice to caregivers of a loved one with TBI and/or PTSD — from simply trying to see how that person's life has changed to helping him get involved in confidence-boosting activities.

There will be Purple Hearts awarded to troops injured during the Jan. 8 Iranian missile barrage on the al-Asad airbase in Iraq, a defense official told Military Times.

The Biodiversity Photography Contest has as main objective to promote the theme of biological natural heritage, namely the natural regions, the ecosystems, the habitats and [...]

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Ditch the idea of yourself as a starving artist. Throw away the notion that you’re doomed to be another poor creative soul. My long time pal Ramit Sethi is back on the show to remind us we need to get back on track to building and living a rich life. And believe me, that doesn’t have to mean cutting back the lattes. Ramit has been on the show a few times, but if you haven’t caught up yet, let me fill you in. Ramit Sethi is the author of the NYT bestseller “I Will Teach You To Be Rich” and writes for over 500,000 monthly readers on his website, iwillteachyoutoberich.com. It’s one of my favorite go-to finance resources covering psychology, personal finance, careers, and entrepreneurship. No one has single-handedly given me better insight into the business side of art, than Ramit. Ramit has updated & expanded 2nd edition of his book and joined me for a LIVE studio conversation on money confessions. In this episode we get into: A rich life isn’t only about save money, it’s about defining & prioritizing the things you love the most. It’s one thing to manage our own personal finances but navigating that with […]

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When it was time to think about the cover – the whole design package – for my NEW BOOK, Creative Calling, I knew I wanted it to be something different. After all…see if you follow me here… it’s just wrong to make a book about creativity with just any old trend, cliche book cover.  Instead, the package needed to embody the ideas within. So when we approached this design challenge of a hard bound book – it had to be meaningful, beautiful, AND stand out in a sea of other books on the shelf.  No small task… And consider this:  you know that this isn’t just a nice story about the book cover.  This is a metaphor for any creative challenge.  Like every episode of podcast is full of practical advice….this is the real life story of ups and downs on this process…on how we struggled to overcame the challenge front of us… with costs, design options, time, publisher feedback, and other real-life constraints.  In short of EVERY CREATIVE PROCESS.  I’ve included 2 live-recorded phone calls with the designers on the project, Lou and Vasco, so you get their take on the creation process, challenges, the concepts behind what we set out to […]

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Today’s episode is going to rock your world … pun fully intended because today’s guest is an actual rock star. You may remember a band called Presidents of the United States of America. They took the world by storm in 1995 with their self titled album, Presidents of the United States of America playing songs like Lump and Peaches. Yes, that’s right. My guest today is frontman Chris Ballew. Chris and I have been friends for years, including collaborating on a music video together and at least one live performance (gotta listen to find out ;). Of course we get into his musical journey, a meteoric rise to success, and then realizing something was missing. We take some deep dives into Chris’ creative process, including his method for capturing his small bits and later using those to write new works, including his new project Casper Babypants. In this episode: Consider what kind of artist you are and how you relate to other artists. For years Chris played in bands, but what he learned about himself is his work is actually solo. Don’t censor yourself while you’re creating. Get it out, no matter how crazy or ridiculous or unusual and then […]

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Debbie Millman is one of my dear friends, a powerhouse creative and someone who inspires me every day. When I was developing my online companion class to the Creative Calling book, of course I had to ask Debbie to join me on stage for a conversation around designing our life with intention. Debbie’s insight is pure gold. AND – this is just one of the segments from the class. If you already have my book, you can access the entire class for free. All you need to do is visit www.creativelive.com/creativecalling and sign up there. Enjoy! FOLLOW DEBBIE: instagram | twitter | website Listen to the Podcast Subscribe   This podcast is brought to you by CreativeLive. CreativeLive is the world’s largest hub for online creative education in photo/video, art/design, music/audio, craft/maker, money/life and the ability to make a living in any of those disciplines. They are high quality, highly curated classes taught by the world’s top experts — Pulitzer, Oscar, Grammy Award winners, New York Times best selling authors and the best entrepreneurs of our times.

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It’s 2018, and traditional marketing concept has shifted. We often hear that content marketing is taking the top and is the future of marketing. While content marketing doesn’t only mean blogging, blog posts on a product, service or about your business, should be a big part of your content marketing strategy. There are vast amounts …

Five Aspects of a Successful Blog Post Read More »

Taking your first steps in programming is like picking up a foreign language. At first, the syntax makes no sense, the vocabulary is unfamiliar, and everything looks and sounds unintelligible. If you’re anything like me when I started, fluency feels impossible. I promise it isn’t. When I began coding, the learning curve hit me — hard. I spent ten months teaching myself the basics while trying to stave off feelings of self-doubt that I now recognize as imposter syndrome.

Mirage JS is helping simplify modern front-end development by providing the ability for front-end engineers to craft applications without relying on an actual back-end service. In this article, I’ll be taking a framework-agnostic approach to show you Mirage JS models and associations. If you haven’t heard of Mirage JS, you can read my previous article in which I introduce it and also integrate it with the progressive framework Vue.js.

In these strange times when everything is connected, it’s too easy to feel lonely and detached. Yes, everybody is just one message away, but there is always something in the way — deadlines to meet, Slack messages to reply, or urgent PRs to review. Connections need time and space to grow, just like learning, and conferences are a great way to find that time and that space. In fact, with SmashingConfs, we’ve always been trying to create such friendly and inclusive spaces.

Prolific is a crowd-sourcing platform for running studies. In contrast to the widely-used Mechanical Turk, it’s specific to studies, has a much better interface, pricing that’s fair to participants, and useful filters to find the right people for your study. Amazon's Mechanical Turk is used for many empirical studies published in the visualization literature, but […]

We provide an explicit construction for a class of commutative, non-associative algebras for each of the simple Chevalley groups of simply laced type. Moreover, we equip these algebras with an associating bilinear form, which turns them into Frobenius algebras. This class includes a 3876-dimensional algebra on which the Chevalley group of type E8 acts by automorphisms. We also prove that these algebras admit the structure of (axial) decomposition algebras.

Applying the equivariant moving frames method, we construct convergent normal forms for real-analytic 5-dimensional totally nondegenerate CR submanifolds of C^4. These CR manifolds are divided into several biholomorphically inequivalent subclasses, each of which has its own complete normal form. Moreover it is shown that, biholomorphically, Beloshapka's cubic model is the unique member of this class with the maximum possible dimension seven of the corresponding algebra of infinitesimal CR automorphisms. Our results are also useful in the study of biholomorphic equivalence problem between CR manifolds, in question.

We derive the non-relativistic $c oinfty$ and ultra-relativistic $c o 0$ limits of the $kappa$-deformed symmetries and corresponding spacetime in (3+1) dimensions, with and without a cosmological constant. We apply the theory of Lie bialgebra contractions to the Poisson version of the $kappa$-(A)dS quantum algebra, and quantize the resulting contracted Poisson-Hopf algebras, thus giving rise to the $kappa$-deformation of the Newtonian (Newton-Hooke and Galilei) and Carrollian (Para-Poincar'e, Para-Euclidean and Carroll) quantum symmetries, including their deformed quadratic Casimir operators. The corresponding $kappa$-Newtonian and $kappa$-Carrollian noncommutative spacetimes are also obtained as the non-relativistic and ultra-relativistic limits of the $kappa$-(A)dS noncommutative spacetime. These constructions allow us to analyze the non-trivial interplay between the quantum deformation parameter $kappa$, the curvature parameter $eta$ and the speed of light parameter $c$.

In this paper we design suboptimal control laws for an unknown linear system on the basis of measured data. We focus on the suboptimal linear quadratic regulator problem and the suboptimal H2 control problem. For both problems, we establish conditions under which a given data set contains sufficient information for controller design. We follow up by providing a data-driven parameterization of all suboptimal controllers. We will illustrate our results by numerical simulations, which will reveal an interesting trade-off between the number of collected data samples and the achieved controller performance.

Motivated by quotient algorithms, such as the well-known $p$-quotient or solvable quotient algorithms, we describe how to compute extensions $ ilde H$ of a finite group $H$ by a direct sum of isomorphic simple $mathbb{Z}_p H$-modules such that $H$ and $ ilde H$ have the same number of generators. Similar to other quotient algorithms, our description will be via a suitable covering group of $H$. Defining this covering group requires a study of the representation module, as introduced by Gasch"utz in 1954. Our investigation involves so-called Fox derivatives (coming from free differential calculus) and, as a by-product, we prove that these can be naturally described via a wreath product construction. An important application of our results is that they can be used to compute, for a given epimorphism $G o H$ and simple $mathbb{Z}_p H$-module $V$, the largest quotient of $G$ that maps onto $H$ with kernel isomorphic to a direct sum of copies of $V$. For this we also provide a description of how to compute second cohomology groups for the (not necessarily solvable) group $H$, assuming a confluent rewriting system for $H$. To represent the corresponding group extensions on the computer, we introduce a new hybrid format that combines this rewriting system with the polycyclic presentation of the module.

We prove the following result: Let $(M,g_0)$ be a compact manifold of dimension $ngeq 12$ with positive isotropic curvature. Then $M$ is diffeomorphic to a spherical space form, or a compact quotient manifold of $mathbb{S}^{n-1} imes mathbb{R}$ by diffeomorphisms, or a connected sum of a finite number of such manifolds. This extends a recent work of Brendle, and implies a conjecture of Schoen in dimensions $ngeq 12$. The proof uses Ricci flow with surgery on compact orbifolds with isolated singularities.

The Gabriel-Roiter measure is used to give an alternative proof of the finiteness of the representation dimension for Artin algebras, a result established by Iyama in 2002. The concept of Gabriel-Roiter measure can be extended to abelian length categories and every such category has multiple Gabriel-Roiter measures. Using this notion, we prove the following broader statement: given any object $X$ and any Gabriel-Roiter measure $mu$ in an abelian length category $mathcal{A}$, there exists an object $X'$ which depends on $X$ and $mu$, such that $Gamma = operatorname{End}_{mathcal{A}}(X oplus X')$ has finite global dimension. Analogously to Iyama's original results, our construction yields quasihereditary rings and fits into the theory of rejective chains.

We prove an inequality between the sum of the Betti numbers of a complex projective manifold and its total curvature, and we characterize the complex projective manifolds whose total curvature is minimal. These results extend the classical theorems of Chern and Lashof to complex projective space.

We prove the effectiveness of the canonical bundle of several Hurwitz spaces of degree k covers of the projective line from curves of genus 13<g<20.

We consider the stochastic 2-dimensional Cahn-Hilliard equation which is driven by the derivative in space of a space-time white noise. We use two different approaches to study this equation. First we prove that there exists a unique solution $Y$ to the shifted equation (see (1.4) below), then $X:=Y+{Z}$ is the unique solution to stochastic Cahn-Hilliard equaiton, where ${Z}$ is the corresponding O-U process. Moreover, we use Dirichlet form approach in cite{Albeverio:1991hk} to construct the probabilistically weak solution the the original equation (1.1) below. By clarifying the precise relation between the solutions obtained by the Dirichlet forms aprroach and $X$, we can also get the restricted Markov uniquness of the generator and the uniqueness of martingale solutions to the equation (1.1).

Let $f colon X o X$ be a surjective endomorphism of a normal projective surface. When $operatorname{deg} f geq 2$, applying an (iteration of) $f$-equivariant minimal model program (EMMP), we determine the geometric structure of $X$. Using this, we extend the second author's result to singular surfaces to the extent that either $X$ has an $f$-invariant non-constant rational function, or $f$ has infinitely many Zariski-dense forward orbits; this result is also extended to Adelic topology (which is finer than Zariski topology).

Positive geometries encode the physics of scattering amplitudes in flat space-time and the wavefunction of the universe in cosmology for a large class of models. Their unique canonical forms, providing such quantum mechanical observables, are characterised by having only logarithmic singularities along all the boundaries of the positive geometry. However, physical observables have logarithmic singularities just for a subset of theories. Thus, it becomes crucial to understand whether a similar paradigm can underlie their structure in more general cases. In this paper we start a systematic investigation of a geometric-combinatorial characterisation of differential forms with non-logarithmic singularities, focusing on projective polytopes and related meromorphic forms with multiple poles. We introduce the notions of covariant forms and covariant pairings. Covariant forms have poles only along the boundaries of the given polytope; moreover, their leading Laurent coefficients along any of the boundaries are still covariant forms on the specific boundary. Whereas meromorphic forms in covariant pairing with a polytope are associated to a specific (signed) triangulation, in which poles on spurious boundaries do not cancel completely, but their order is lowered. These meromorphic forms can be fully characterised if the polytope they are associated to is viewed as the restriction of a higher dimensional one onto a hyperplane. The canonical form of the latter can be mapped into a covariant form or a form in covariant pairing via a covariant restriction. We show how the geometry of the higher dimensional polytope determines the structure of these differential forms. Finally, we discuss how these notions are related to Jeffrey-Kirwan residues and cosmological polytopes.

Let the group $G = AB$ be the product of subgroups $A$ and $B$, and let $p$ be a prime. We prove that $p$ does not divide the conjugacy class size (index) of each $p$-regular element of prime power order $xin Acup B$ if and only if $G$ is $p$-decomposable, i.e. $G=O_p(G) imes O_{p'}(G)$.

In cite{CC} the authors, investigating a model of population dynamics, find the following result. Let $Omegasubset mathbb{R}^N$, $Ngeq 1$, be a bounded smooth domain. The weighted eigenvalue problem $-Delta u =lambda m u $ in $Omega$ under homogeneous Dirichlet boundary conditions, where $lambda in mathbb{R}$ and $min L^infty(Omega)$, is considered. The authors prove the existence of minimizers $check m$ of the principal positive eigenvalue $lambda_1(m)$ when $m$ varies in a class $mathcal{M}$ of functions where average, maximum, and minimum values are given. A similar result is obtained in cite{CCP} when $m$ is in the class $mathcal{G}(m_0)$ of rearrangements of a fixed $m_0in L^infty(Omega)$. In our work we establish that, if $Omega$ is Steiner symmetric, then every minimizer in cite{CC,CCP} inherits the same kind of symmetry.

In cite{S 2017}, Suh gave a non-existence theorem for Hopf real hypersurfaces in the complex quadric with parallel normal Jacobi operator. Motivated by this result, in this paper, we introduce some generalized conditions named $mathcal C$-parallel or Reeb parallel normal Jacobi operators. By using such weaker parallelisms of normal Jacobi operator, first we can assert a non-existence theorem of Hopf real hypersurfaces with $mathcal C$-parallel normal Jacobi operator in the complex quadric $Q^{m}$, $m geq 3$. Next, we prove that a Hopf real hypersurface has Reeb parallel normal Jacobi operator if and only if it has an $mathfrak A$-isotropic singular normal vector field.

We define local indices for projective umbilics and godrons (also called cusps of Gauss) on generic smooth surfaces in projective 3-space. By means of these indices, we provide formulas that relate the algebraic numbers of those characteristic points on a surface (and on domains of the surface) with the Euler characteristic of that surface (resp. of those domains). These relations determine the possible coexistences of projective umbilics and godrons on the surface. Our study is based on a "fundamental cubic form" for which we provide a closed simple expression.

Given spherically symmetric characteristic initial data for the Einstein-scalar field system with a positive cosmological constant, we provide a criterion, in terms of the dimensionless size and dimensionless renormalized mass content of an annular region of the data, for the formation of a future trapped surface. This corresponds to an extension of Christodoulou's classical criterion by the inclusion of the cosmological term.

We construct a 2-equivalence $mathfrak{CohTheory}^ ext{op} simeq mathfrak{TypeSpaceFunc}$. Here $mathfrak{CohTheory}$ is the 2-category of positive theories and $mathfrak{TypeSpaceFunc}$ is the 2-category of type space functors. We give a precise definition of interpretations for positive logic, which will be the 1-cells in $mathfrak{CohTheory}$. The 2-cells are definable homomorphisms. The 2-equivalence restricts to a duality of categories, making precise the philosophy that a theory is `the same' as the collection of its type spaces (i.e. its type space functor).

In characterising those functors that arise as type space functors, we find that they are specific instances of (coherent) hyperdoctrines. This connects two different schools of thought on the logical structure of a theory.

The key ingredient, the Deligne completeness theorem, arises from topos theory, where positive theories have been studied under the name of coherent theories.

We introduce a Gaussian measure formally preserved by the 2-dimensional Primitive Equations driven by additive Gaussian noise. Under such measure the stochastic equations under consideration are singular: we propose a solution theory based on the techniques developed by Gubinelli and Jara in cite{GuJa13} for a hyperviscous version of the equations.

In this paper we construct an equivariant embedding of the affine space $mathbb{A}^n$ with the translation group action into a complete non-projective algebraic variety $X$ for all $n geq 3$. The theory of toric varieties is used as the main tool for this construction. In the case of $n = 3$ we describe the orbit structure on the variety $X$.

The problem of minimizing an entropy functional subject to linear constraints is a useful example of partially finite convex programming. In the 1990s, Borwein and Lewis provided broad and easy-to-verify conditions that guarantee strong duality for such problems. Their approach is to construct a function in the quasi-relative interior of the relevant infinite-dimensional set, which assures the existence of a point in the core of the relevant finite-dimensional set. We revisit this problem, and provide an alternative proof by directly appealing to the definition of the core, rather than by relying on any properties of the quasi-relative interior. Our approach admits a minor relaxation of the linear independence requirements in Borwein and Lewis' framework, which allows us to work with certain piecewise-defined moment functions precluded by their conditions. We provide such a computed example that illustrates how this relaxation may be used to tame observed Gibbs phenomenon when the underlying data is discontinuous. The relaxation illustrates the understanding we may gain by tackling partially-finite problems from both the finite-dimensional and infinite-dimensional sides. The comparison of these two approaches is informative, as both proofs are constructive.

Recent studies of optimization methods and GNC of spacecraft near small bodies focusing on descent, landing, rendezvous, etc., with key safety constraints such as line-of-sight conic zones and soft landings have shown promising results; this paper considers descent missions to an asteroid surface with a constraint that consists of an onboard camera and asteroid surface markers while using a stochastic convex MPC law. An undermodeled asteroid gravity and spacecraft technology inspired measurement model is established to develop the constraint. Then a computationally light stochastic Linear Quadratic MPC strategy is presented to keep the spacecraft in satisfactory field of view of the surface markers while trajectory tracking, employing chance based constraints and up-to-date estimation uncertainty from navigation. The estimation uncertainty giving rise to the tightened constraints is particularly addressed. Results suggest robust tracking performance across a variety of trajectories.

We derive sufficient conditions for exponential decay of solutions of the delay negative feedback equation with distributed delay. The conditions are written in terms of exponential moments of the distribution. Our method only uses elementary tools of calculus and is robust towards possible extensions to more complex settings, in particular, systems of delay differential equations. We illustrate the applicability of the method to particular distributions - Dirac delta, Gamma distribution, uniform and truncated normal distributions.

We prove that all non-degenerate relative equilibria of the planar Newtonian $n$--body problem can be continued to spaces of constant curvature $kappa$, positive or negative, for small enough values of this parameter. We also compute the extension of some classical relative equilibria to curved spaces using numerical continuation. In particular, we extend Lagrange's triangle configuration with different masses to both positive and negative curvature spaces.

In this work we study the dynamical behavior Tonelli Lagrangian systems defined on the tangent bundle of the torus $mathbb{T}^2=mathbb{R}^2 / mathbb{Z}^2$. We prove that the Lagrangian flow restricted to a high energy level $ E_L^{-1}(c)$ (i.e $ c> c_0(L)$) has positive topological entropy if the flow satisfies the Kupka-Smale propriety in $ E_L^{-1}(c)$ (i.e, all closed orbit with energy $c$ are hyperbolic or elliptic and all heteroclinic intersections are transverse on $E_L^{-1}(c)$). The proof requires the use of well-known results in Aubry-Mather's Theory.

In this paper we study manifolds $M_{Sigma}$ with fibered singularities, more specifically, a relevant space $Riem^{psc}(X_{Sigma})$ of Riemannian metrics with positive scalar curvature. Our main goal is to prove that the space $Riem^{psc}(X_{Sigma})$ is homotopy invariant under certain surgeries on $M_{Sigma}$.