We study SLE$_{kappa}$ theory with elements of Quasi-Sure Stochastic Analysis through Aggregation. Specifically, we show how the latter can be used to construct the SLE$_{kappa}$ traces quasi-surely (i.e. simultaneously for a family of probability measures with certain properties) for $kappa in mathcal{K}cap mathbb{R}_+ setminus ([0, epsilon) cup {8})$, for any $epsilon>0$ with $mathcal{K} subset mathbb{R}_{+}$ a nontrivial compact interval, i.e. for all $kappa$ that are not in a neighborhood of zero and are different from $8$. As a by-product of the analysis, we show in this language a version of the continuity in $kappa$ of the SLE$_{kappa}$ traces for all $kappa$ in compact intervals as above.

We present the correspondence between Lax integrable systems with spectral parameter on a Riemann surface, and Conformal Field Theories, in quite general set-up suggested earlier by the author. This correspondence turns out to give a prequantization of the integrable systems in question.

Domain of mathematical logic in computers is dominated by automated theorem provers (ATP) and interactive theorem provers (ITP). Both of these are hard to access by AI from the human-imitation approach: ATPs often use human-unfriendly logical foundations while ITPs are meant for formalizing existing proofs rather than problem solving. We aim to create a simple human-friendly logical system for mathematical problem solving. We picked the case study of Euclidean geometry as it can be easily visualized, has simple logic, and yet potentially offers many high-school problems of various difficulty levels. To make the environment user friendly, we abandoned strict logic required by ITPs, allowing to infer topological facts from pictures. We present our system for Euclidean geometry, together with a graphical application GeoLogic, similar to GeoGebra, which allows users to interactively study and prove properties about the geometrical setup.

We establish versions of Conley's (i) fundamental theorem and (ii) decomposition theorem for a broad class of hybrid dynamical systems. The hybrid version of (i) asserts that a globally-defined "hybrid complete Lyapunov function" exists for every hybrid system in this class. Motivated by mechanics and control settings where physical or engineered events cause abrupt changes in a system's governing dynamics, our results apply to a large class of Lagrangian hybrid systems (with impacts) studied extensively in the robotics literature. Viewed formally, these results generalize those of Conley and Franks for continuous-time and discrete-time dynamical systems, respectively, on metric spaces. However, we furnish specific examples illustrating how our statement of sufficient conditions represents merely an early step in the longer project of establishing what formal assumptions can and cannot endow hybrid systems models with the topologically well characterized partitions of limit behavior that make Conley's theory so valuable in those classical settings.

We show that the traveling salesman problem (TSP) and its many variants may be modeled as functional optimization problems over a graph. In this formulation, all vertices and arcs of the graph are functionals; i.e., a mapping from a space of measurable functions to the field of real numbers. Many variants of the TSP, such as those with neighborhoods, with forbidden neighborhoods, with time-windows and with profits, can all be framed under this construct. In sharp contrast to their discrete-optimization counterparts, the modeling constructs presented in this paper represent a fundamentally new domain of analysis and computation for TSPs and their variants. Beyond its apparent mathematical unification of a class of problems in graph theory, the main advantage of the new approach is that it facilitates the modeling of certain application-specific problems in their home space of measurable functions. Consequently, certain elements of economic system theory such as dynamical models and continuous-time cost/profit functionals can be directly incorporated in the new optimization problem formulation. Furthermore, subtour elimination constraints, prevalent in discrete optimization formulations, are naturally enforced through continuity requirements. The price for the new modeling framework is nonsmooth functionals. Although a number of theoretical issues remain open in the proposed mathematical framework, we demonstrate the computational viability of the new modeling constructs over a sample set of problems to illustrate the rapid production of end-to-end TSP solutions to extensively-constrained practical problems.

We investigate learnability of possibilistic theories from entailments in light of Angluin's exact learning model. We consider cases in which only membership, only equivalence, and both kinds of queries can be posed by the learner. We then show that, for a large class of problems, polynomial time learnability results for classical logic can be transferred to the respective possibilistic extension. In particular, it follows from our results that the possibilistic extension of propositional Horn theories is exactly learnable in polynomial time. As polynomial time learnability in the exact model is transferable to the classical probably approximately correct model extended with membership queries, our work also establishes such results in this model.

We study the problem of jointly designing a sparse sensor and actuator schedule for linear dynamical systems while guaranteeing a control/estimation performance that approximates the fully sensed/actuated setting. We further prove a separation principle, showing that the problem can be decomposed into finding sensor and actuator schedules separately. However, it is shown that this problem cannot be efficiently solved or approximated in polynomial, or even quasi-polynomial time for time-invariant sensor/actuator schedules; instead, we develop deterministic polynomial-time algorithms for a time-varying sensor/actuator schedule with guaranteed approximation bounds. Our main result is to provide a polynomial-time joint actuator and sensor schedule that on average selects only a constant number of sensors and actuators at each time step, irrespective of the dimension of the system. The key idea is to sparsify the controllability and observability Gramians while providing approximation guarantees for Hankel singular values. This idea is inspired by recent results in theoretical computer science literature on sparsification.

Emulsions, and processes for making the emulsions, useful for imparting water resistance to gypsum products are disclosed. Process for making the emulsion and gypsum products made from the emulsion are also disclosed. The emulsions of the invention include at least one paraffin wax and a hydrophilic metallic salt. The emulsions of the invention may further include a saponifiable wax substitute for montan wax. The emulsions of the invention may further include a biocide.

Emulsions, and processes for making the emulsions, useful for imparting water resistance to gypsum products are disclosed. Process for making the emulsion and gypsum products made from the emulsion are also disclosed. The emulsions of the invention include at least one paraffin wax and a hydrophilic metallic salt. The emulsions of the invention may further include a saponifiable wax substitute for montan wax. The emulsions of the invention may further include a biocide.

Disclosed are rheology modifiers comprising compositionally disperse polymeric compositions and/or crystallinity disperse polymeric compositions that may be useful in modifying the rheological properties of lubrication fluids, and methods for making such compositions. The compositionally disperse polymeric composition are formed from at least two discrete compositions of ethylene copolymers. The crystallinity disperse polymeric composition are formed from ethylene copolymers having at least two discrete values of residual crystallinity.

An inner cannula (20) for a tracheostomy tube assembly includes a thin, inner sheath (22) supported externally by a structural frame (23) having a longitudinal portion (25) and a plurality of ribs (26) extending circumferentially and spaced along the cannula. The inner cannula (20) is inserted within and is removable from an outer tracheostomy tube (1). The inner cannula (20) is made by coating a plastic layer on a core to form the sheath and then placing the sheath on a curved core. The structural frame (23) is then moulded about the sheath (22) in a mould 80.

A rheometer includes a drive shaft, a drag cup motor for rotating the drive shaft, a first measuring object supported by the drive shaft, a second measuring object, a linear position sensor, and processing and control electronics. The linear position sensor includes a target (e.g., an aluminum target) mounted to the drive shaft, and a pair of coils. The linear position sensor is configured to measure thermal expansion of the drive shaft based on a change in impedance of the coils resulting from a displacement of the target relative to the coils. The processing and control electronics are in communication with the coils and are configured to adjust a position of one of the measuring objects relative to the other based on a change in impedance of the coils resulting from a displacement of the target relative to the coils, thereby to maintain a substantially constant measurement gap therebetween.

An article may include a first polymeric material layer having a surface. A first conductive trace may form at least a portion of the first layer surface. The article may further include a second polymeric material layer. The second layer may have a first surface, a portion of the second layer first surface being bonded to a portion of the first layer surface. The second layer may have a portion of a channel defined therein, the channel at least partially coinciding with a portion of the first conductive trace. The article may also include a first patch interposed between the first layer surface and the second layer first surface. The first patch may span the channel and cover a portion of the first conductive trace.

A polymeric housing may have a channel defined therein. A first conductive trace may at least partially coincide with the channel. A first wire may have a first conductor surrounded by a first insulating jacket. The first conductor may be in electrical communication with the first conductive trace. A jacket bonding region of the first jacket may be welded to a housing bonding region of the housing. The jacket bonding region and the housing bonding region may be formed from a common type of polymer.

FORMER Saint Peter Crouch has revealed the "embarrassing" moment Theo Walcott and Nathan Dyer burst onto the scene.

Theo Von, Comedian who's special, "No Offense will be on Netflix soon', joins Joey Diaz and Lee Syatt live in studio.

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Theo Von, Comedian who special "No Offense" is available on Netflix, joins Joey Diaz and Lee Syatt live in studio!

This podcast is brought to you by:

Theo Von, Comedian whose special "No Offense" is available on Netflix and the co-host of the "Allegedly Podcast," joins Joey Diaz and Lee Syatt live in studio!

This podcast is brought to you by:

Theo Von, Comedian, co-host of the "Allegedly Podcast," and host of the "This Past Weekend" podcast, joins Joey Diaz and Lee Syatt live in studio!

This podcast is brought to you by:

Theo Von, Comedian and host of the "This Past Weekend" podcast, joins Joey Diaz and Lee Syatt live in studio!

This podcast is brought to you by:

'How do we distinguish between the Word of God and human tradition? Why is it so important that we make this distinction?'

Multitalented musician Michael Emenau examines some of the benefits and pitfalls of using musical scales and offers some creative practices for using them.

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The post Music Theory Tutorial: Working with Scales appeared first on Dubspot Blog.

'How do we distinguish between the Word of God and human tradition? Why is it so important that we make this distinction?'

Den Ursprung einer Epidemie zu finden ist nicht leicht, sagt Fabian Leendertz. Er jagt seit Jahrzehnten Erreger – und hat die Quelle für Ebola in Westafrika gefunden. Der Forscher erklärt, warum die Suche so schwierig ist und welche Rolle Affen dabei spielen.

Weltweit kursieren inzwischen wilde Theorien, Microsoft-Gründer Bill Gates sei für den Ausbruch des Virus verantwortlich. Seinen Ursprung nahmen die Anschuldigungen in den USA. Doch längst haben sie auch Deutschland erreicht.

Früher gab es pro Dorf ein paar einsame Sonderlinge. Heute sind sie dank sozialer Medien vernetzt. Sie reden von „querdenken“. In Wahrheit suchen sie einfache Antworten auf komplexe Fragen – und sind schnell dabei, für alles einen Schuldigen zu finden.

'How do we distinguish between the Word of God and human tradition? Why is it so important that we make this distinction?'

You win some you lose some, right? It turns out that when it comes to the psychology of winning and losing there is a lot more at play. In part two of our series on the psychology of awards, Two Guys on Your Head, Dr. Art Markman, and Dr. Bob Duke talk about Norm Theory.

"... There shall be famines, and pestilences, and earthquakes in divers places," and so it is... but is the coronavirus one of the seven last plagues ? and is taking precautions against its spread displaying a lack of faith ? Study with the pastors as they speak on this topic in this episode of Bible Answers Live, and you'll learn also of life and family once we all get to Heaven, and what the role of grace is as we strive for a perfect character, before eternity in Heaven.

Mehrere katholische Bischöfe kritisieren die Corona-Maßnahmen und greifen dabei auf weitverbreitete Verschwörungstheorien zurück. Sie sehen den "Auftakt einer Weltregierung". Die Deutsche Bischofskonferenz übt scharfe Kritik.

The new documentary, “Hesburgh,” explores the life of Father Theodore Hesburgh, who served as a long-time president of the University of Notre Dame and is recognized now as one of the most important civic and educational leaders of the 20th … More →

The post PBS NewsHour: Following Father Theodore Hesburgh through Civil Rights era appeared first on Religion & Ethics NewsWeekly.

While reporting financial results for the first quarter on Thursday, aerospace and defense company Raytheon Technologies Corp. (RTX) said it is not providing an outlook at this time, due to the ongoing uncertainty regarding the scope, severity and duration of the COVID-19 pandemic.

Angela Gheorghiu interviewed on the red carpet at The South Bank Sky Arts Awards 2019 at the Savoy Hotel, London on Sunday July 7th.

The Dose and Dr. Brian Goldman separate fact from fiction regarding the rumour that COVID-19 spread to humans after it escaped from a lab in China.

How do you fancy a theory describing everything in the world and the whole universe? Physicists have been trying to find a universal theory for centuries. Progress has been made: BBC’s Jim Al-Khalili describes the three pillars of modern physics: quantum theory, relativity, and thermodynamics. But is physics any closer to finding the ONE theory that explains it all?

A hat possibly belonging to Theo Hayez is found at Cape Byron Lighthouse, near where he was last seen, and sent for forensic testing.

The parents of missing Belgian backpacker Theo Hayez, who disappeared in Byron Bay in May shortly before he was due to fly home, say they are hopeful their son will still be found alive.

The 18-year-old has been missing for over three months, and was last seen in Byron Bay at the end of May.

The hunt for the missing Belgian backpacker, who disappeared after a night out on May 31, is formally referred to the NSW coroner in a move that ends the official police search.

The family of missing backpacker Theo Hayez criticises Belgian media for claiming DNA on a cap found near Cape Byron Lighthouse suggested it was owned by the teen, who has not been seen for almost a year.

After more than four decades of dominance, free-market capitalism is facing a challenge. Its rival, the rather blandly named Modern Monetary Theory, promises to return economic planning to a less ideological footing. It’s also keen to strike a blow against the “surplus fetish” that many economists now blame for declining public services and growing inequality.

MORNING BRIEFING: The father of missing Belgian backpacker Theo Hayez will front the media today as homicide detectives travel to Byron Bay to assist in the investigation, while some of the residents of Mascot Towers will be permitted to return to their homes to pick up belongings.

The father of missing Belgian backpacker Theo Hayez travels to Australia to give an emotional press conference where he promises to bring his son, who has been missing since May 31, home.

The father of missing Belgian backpacker Theo Hayez says unlocking his son's last WhatAsapp messages could be key to find him alive. But a leading expert says the tech giant is incapable of unjumbling the "garbled" encrypted messages.

Police have released CCTV footage of missing backpacker Theo Hayez at a convenience store the night he disappeared.