Some recent developments in theory of fractional positive and cone linear systems

The overview of some recent developments and new results in the theory of fractional positive and cone one-dimensional (1D) and two-dimensional (2D) linear systems are presented in the article. The state equations and their solution for the fractional continuous-time and discrete-time linear systems are given. Necessary and sufficient conditions for the internal and external positivity of the fractional linear systems are established. The reachability of the fractional linear systems is addressed. A new notation of the cone systems is introduced and methods for computation of such systems are proposed. Positive fractional 2D linear systems are intoduced. Necessary and sufficient conditions for the positivity and reachability are established. The considerations are illustrated with many examples of 1D and 2D linear systems.Запропоновано огляд та деякі нові результати у теорії фракційних додатніх та конусних одновимірних (1D) та двовимірних (2D) лінійних систем. Подано рівняння стану та їхнє розв’язання для фракційних неперервних та дискретних лінійних систем. Встановлено необхідні та достатні умови для внутрішньої та зовнішньої додатності фракційних лінійних систем. Показано їхню досяжність. Запропоновано нову форму запису конусних систем та методи, придатні для комп’ютерного розрахунку таких систем. Представлено додатні фракційні 2D лінійні системи. Встановлено необхідні та достатні умови для додатності та досяжності. Теоретичні виклади проілюстровано чисельними прикладами 1D та 2D лінійних систем.Предложены анализ состояния вопроса и некоторые новые результаты, полученные в теории фракционных положительных и конусных одномерных (1D) и двумерных (2D) линейных систем. Приведены уравнения состояния и их решения для фракционных непрерывных и дискретных линейных систем. Выявлены необходимые и достаточные условия для внутренней и внешней положительности фракционных линейных систем. Показана их достижимость. Предложена новая форма записи конусных систем, а также методы их компьютерного расчета. Представлены положительные фракционные 2D линейные системы. Установлены необходимые и достаточные условия для положительности и достижимости. Теоретические выкладки иллюстрированы численными примерами 1D и 1D линейных систем

Fast and Robust Detection of Fallen People from a Mobile Robot

This paper deals with the problem of detecting fallen people lying on the floor by means of a mobile robot equipped with a 3D depth sensor. In the proposed algorithm, inspired by semantic segmentation techniques, the 3D scene is over-segmented into small patches. Fallen people are then detected by means of two SVM classifiers: the first one labels each patch, while the second one captures the spatial relations between them. This novel approach showed to be robust and fast. Indeed, thanks to the use of small patches, fallen people in real cluttered scenes with objects side by side are correctly detected. Moreover, the algorithm can be executed on a mobile robot fitted with a standard laptop making it possible to exploit the 2D environmental map built by the robot and the multiple points of view obtained during the robot navigation. Additionally, this algorithm is robust to illumination changes since it does not rely on RGB data but on depth data. All the methods have been thoroughly validated on the IASLAB-RGBD Fallen Person Dataset, which is published online as a further contribution. It consists of several static and dynamic sequences with 15 different people and 2 different environments

Global Phase Diagram of the Kondo Lattice: From Heavy Fermion Metals to Kondo Insulators

We discuss the general theoretical arguments advanced earlier for the T=0 global phase diagram of antiferromagnetic Kondo lattice systems, distinguishing between the established and the conjectured. In addition to the well-known phase of a paramagnetic metal with a "large" Fermi surface (P_L), there is also an antiferromagnetic phase with a "small" Fermi surface (AF_S). We provide the details of the derivation of a quantum non-linear sigma-model (QNLsM) representation of the Kondo lattice Hamiltonian, which leads to an effective field theory containing both low-energy fermions in the vicinity of a Fermi surface and low-energy bosons near zero momentum. An asymptotically exact analysis of this effective field theory is made possible through the development of a renormalization group procedure for mixed fermion-boson systems. Considerations on how to connect the AF_S and P_L phases lead to a global phase diagram, which not only puts into perspective the theory of local quantum criticality for antiferromagnetic heavy fermion metals, but also provides the basis to understand the surprising recent experiments in chemically-doped as well as pressurized YbRh2Si2. We point out that the AF_S phase still occurs for the case of an equal number of spin-1/2 local moments and conduction electrons. This observation raises the prospect for a global phase diagram of heavy fermion systems in the Kondo-insulator regime. Finally, we discuss the connection between the Kondo breakdown physics discussed here for the Kondo lattice systems and the non-Fermi liquid behavior recently studied from a holographic perspective.Comment: (v3) leftover typos corrected. (v2) Published version. 32 pages, 4 figures. Section 7, on the connection between the Kondo lattice systems and the holographic models of non-Fermi liquid, is expanded. (v1) special issue of JLTP on quantum criticalit

Recent developments in planet migration theory

Planetary migration is the process by which a forming planet undergoes a drift of its semi-major axis caused by the tidal interaction with its parent protoplanetary disc. One of the key quantities to assess the migration of embedded planets is the tidal torque between the disc and planet, which has two components: the Lindblad torque and the corotation torque. We review the latest results on both torque components for planets on circular orbits, with a special emphasis on the various processes that give rise to additional, large components of the corotation torque, and those contributing to the saturation of this torque. These additional components of the corotation torque could help address the shortcomings that have recently been exposed by models of planet population syntheses. We also review recent results concerning the migration of giant planets that carve gaps in the disc (type II migration) and the migration of sub-giant planets that open partial gaps in massive discs (type III migration).Comment: 52 pages, 18 figures. Review article to be published in "Tidal effects in Astronomy and Astrophysics", Lecture Notes in Physic

Litigation Isolationism

Over the past two decades, U.S. courts have pursued a studied avoidance of transnational litigation. The resulting litigation isolationism appears to be driven by courts’ desire to promote separation of powers, international comity, and the interests of defendants. This Article demonstrates, however, that this new kind of “avoidance” in fact frequently undermines not only these values but also other significant U.S. interests by continuing to interfere with foreign relations and driving plaintiffs to sue in foreign courts. This Article offers four contributions: First, it focuses the conversation about transnational litigation on those doctrines designed to avoid it—that is, doctrines that permit or require courts to dismiss a case based on its “foreignness.” Doing so helps to identify the particular concerns justifying this kind of avoidance and to evaluate them on their own terms. Second, the Article presents evidence of emerging foreign trends that increasingly (and surprisingly) permit traditionally American, plaintiff-friendly procedures, including higher damages awards, aggregate litigation, and third-party litigation financing. Third, the Article demonstrates that, particularly in light of these foreign trends, avoidance has failed to achieve its stated goals, and in many instances has undermined them. Finally, the Article suggests ways to refine avoidance doctrines to address these unintended consequences. Its more basic and urgent task, however, is to identify the growing phenomenon of litigation isolationism, highlight its perversities, and caution against its further expansion

The Dimensions of Field Theory : From Particles to Strings

This is an editorial summary of the contents of a Book comprising a set of Articles by acknowledged experts dealing with the impact of Field Theory on major areas of physics (from elementary particles through condensed matter to strings), arranged subjectwise under six broad heads. The Book which emphasizes the conceptual, logical and formal aspects of the state of the art in these respective fields, carries a Foreword by Freeman Dyson, and is to be published by the Indian National Science Academy on the occasion of the International Mathematical Year 2000. The authors and full titles of all the Articles (33) are listed sequentially (in the order of their first appearance in the narration) under the bibliography at the end of this Summary, while a few of the individual articles to appear in the Book are already available on the LANL internet.Comment: LaTex file, 24 page