Bulk-Edge Correspondence in the Entanglement Spectra

Li and Haldane conjectured and numerically substantiated that the entanglement spectrum of the reduced density matrix of ground-states of time-reversal breaking topological phases (fractional quantum Hall states) contains information about the counting of their edge modes when the ground-state is cut in two spatially distinct regions and one of the regions is traced out. We analytically substantiate this conjecture for a series of FQH states defined as unique zero modes of pseudopotential Hamiltonians by finding a one to one map between the thermodynamic limit counting of two different entanglement spectra: the particle entanglement spectrum, whose counting of eigenvalues for each good quantum number is identical (up to accidental degeneracies) to the counting of bulk quasiholes, and the orbital entanglement spectrum (the Li-Haldane spectrum). As the particle entanglement spectrum is related to bulk quasihole physics and the orbital entanglement spectrum is related to edge physics, our map can be thought of as a mathematically sound microscopic description of bulk-edge correspondence in entanglement spectra. By using a set of clustering operators which have their origin in conformal field theory (CFT) operator expansions, we show that the counting of the orbital entanglement spectrum eigenvalues in the thermodynamic limit must be identical to the counting of quasiholes in the bulk. The latter equals the counting of edge modes at a hard-wall boundary placed on the sample. Moreover, we show this to be true even for CFT states which are likely bulk gapless, such as the Gaffnian wavefunction.Comment: 20 pages, 6 figure

Haldane Statistics in the Finite Size Entanglement Spectra of Laughlin States

We conjecture that the counting of the levels in the orbital entanglement spectra (OES) of finite-sized Laughlin Fractional Quantum Hall (FQH) droplets at filling $\nu=1/m$ is described by the Haldane statistics of particles in a box of finite size. This principle explains the observed deviations of the OES counting from the edge-mode conformal field theory counting and directly provides us with a topological number of the FQH states inaccessible in the thermodynamic limit- the boson compactification radius. It also suggests that the entanglement gap in the Coulomb spectrum in the conformal limit protects a universal quantity- the statistics of the state. We support our conjecture with ample numerical checks.Comment: 4.1 pages, published versio

Hyperostotic tympanic bone spicules in domestic and wild animal species

Hyperostotic tympanic bone spicules (HTBS), or "mucoperiosteal exostoses" (ME, syn.) are small, globular (>= 1 mm in diameter), mostly stalked and drumstick-like, bony structures, which arise from the inner wall of the tympanic bulla and project into the middle ear cavity. HTBS present as mineral densities inside the tympanic bulla on radiographs or computed tomographic (CT) images. They have previously been referred to as "otoliths" and were thought to represent mineral concretions secondary to otitis media. Recently, it was shown that HTBS actually consist of regularly composed bone tissue, covered by normal middle ear mucosa. So far, HTBS have only extensively been described in dogs, where they occur with a prevalence of up to >45%. A recent study detected ME, most likely representing HTBS, in the tympanic cavities of skeletonised skull bones of African lions. To estimate the occurrence of HTBS in other mammal species, the middle ears of adult animals of 78 different domestic, wild, and zoo species undergoing routine necropsy at the Institute of Veterinary Pathology of the LMU Munich, Germany were examined in the present study. HTBS were found in the tympanic bullae of carnivorous species, such as canids (wolf, fox), and in several large felid species (lion, tiger, leopard, cheetah). In contrast, HTBS were not present in domestic cats (more than to 200 cases), small carnivorous species such as mustelids, nor in any primate, ungulate, ruminant, pig, insectivore, or rodent species. The detectability of HTBS by CT of the tympanic bullae of large felids was demonstrated in an African lion. Histologically, HTBS consisted of mature lamellar bone, covered by periosteum and a partially ciliated, flat epithelium, regularly without any apparent inflammatory alterations. The present study demonstrates that HTBS may frequently occur in large felids and in different canid species. These findings should be taken into account when examining the middle ear, or interpreting bulla radiographs/CT-images of the respective species. However, the factors triggering the development of HTBS remain to be identified

The influence of holes in the mechanical properties of EWT solar cells

EWT back contact solar cells are manufactured from very thin silicon wafers. These wafers are drilled by means of a laser process creating a matrix of tiny holes with a density of approximately 125 holes per square centimeter. Their influence in the stiffness and mechanical strength has been studied. To this end, both wafers with and without holes have been tested with the ring on ring test. Numerical simulations of the tests have been carried out through the Finite Element Method taking into account the non-linearities present in the tests. It's shown that one may use coarse meshes without holes to simulate the test and after that sub models are used for the estimation of the stress concentration around the holes

Microscopic theory of the quantum Hall hierarchy

We solve the quantum Hall problem exactly in a limit and show that the ground states can be organized in a fractal pattern consistent with the Haldane-Halperin hierarchy, and with the global phase diagram. We present wave functions for a large family of states, including those of Laughlin and Jain and also for states recently observed by Pan {\it et. al.}, and show that they coincide with the exact ones in the solvable limit. We submit that they establish an adiabatic continuation of our exact results to the experimentally accessible regime, thus providing a unified approach to the hierarchy states.Comment: 4 pages, 2 figures. Publishe

Bisimulation of Labeled State-to-Function Transition Systems of Stochastic Process Languages

Labeled state-to-function transition systems, FuTS for short, admit multiple transition schemes from states to functions of finite support over general semirings. As such they constitute a convenient modeling instrument to deal with stochastic process languages. In this paper, the notion of bisimulation induced by a FuTS is proposed and a correspondence result is proven stating that FuTS-bisimulation coincides with the behavioral equivalence of the associated functor. As generic examples, the concrete existing equivalences for the core of the process algebras ACP, PEPA and IMC are related to the bisimulation of specific FuTS, providing via the correspondence result coalgebraic justification of the equivalences of these calculi.Comment: In Proceedings ACCAT 2012, arXiv:1208.430

Distributed Synthesis in Continuous Time

We introduce a formalism modelling communication of distributed agents strictly in continuous-time. Within this framework, we study the problem of synthesising local strategies for individual agents such that a specified set of goal states is reached, or reached with at least a given probability. The flow of time is modelled explicitly based on continuous-time randomness, with two natural implications: First, the non-determinism stemming from interleaving disappears. Second, when we restrict to a subclass of non-urgent models, the quantitative value problem for two players can be solved in EXPTIME. Indeed, the explicit continuous time enables players to communicate their states by delaying synchronisation (which is unrestricted for non-urgent models). In general, the problems are undecidable already for two players in the quantitative case and three players in the qualitative case. The qualitative undecidability is shown by a reduction to decentralized POMDPs for which we provide the strongest (and rather surprising) undecidability result so far

Distributed On-Demand Routing for LEO Mega-Constellations: A Starlink Case Study

The design and launch of large-scale satellite networks create an imminent demand for efficient and delay-minimising routing methods. With the rising number of satellites in such constellations, pre-computing all shortest routes between all satellites and for all times becomes more and more infeasible due to space and time limitations. Even though distributed on-demand routing methods were developed for specific LEO satellite network configurations, they are not suited for increasingly popular mega-constellations based on Walker Delta formations. The contributions of this paper are twofold. First, we introduce a formal model that mathematically captures the time-evolving locations of satellites in a Walker Delta constellation and use it to establish a formula to compute the minimum number of ISL hops between two given satellites. In the second part, we present an on-demand hop-count-based routing algorithm that approximates the optimal path while achieving superior performance compared to classical shortest-path algorithms like Dijkstra.Comment: This is an extended version of a paper published in ASMS/SPSC 2022 containing proofs and further detail

Dynamic factors for underpasses in high speed train lines

Los pasos inferiores son muy numerosos en las líneas de ferrocarril. Su comportamiento dinámico ha recibido mucha menos atención que el de otras estructuras como los puentes, pero su elevado número hace que su estudio sea económicamente relevante con vista a optimizar su forma, manteniendo la seguridad. El proyecto de puentes según el Eurocódigo incluye comprobaciones de estados límite de tensiones bajo carga dinámica. En el caso de pasos inferiores, las comprobaciones pueden resultar tan costosas como aquellas de puentes, pese a que su coste es mucho menor. Por tanto, se impone la búsqueda de unas reglas de cálculo simplificado que pongan en consonancia el coste de la estructura con el esfuerzo necesario para su proyecto. Este artículo propone un conjunto de reglas basadas en un estudio paramétrico.Underpasses are common in modern railway lines. Wildlife corridors and drainage conduits often fall into this category of partially buried structures. Their dynamic behavior has received far less attention than that of other structures such as bridges, but their large number makes their study an interesting challenge from the viewpoint of safety and cost savings. The bridge design rules in accordance with the Eurocode involve checks on stresses according to dynamic loading. In the case of underpasses, those checks may be as much as those for bridges. Therefore, simplified design rules may align the design effort with their cost. Such a set of rules may provide estimations of response parameters based on the key parameters influencing the result. This paper contains a proposal based on a parametric study.Peer Reviewe

A Hierarchy of Scheduler Classes for Stochastic Automata

Stochastic automata are a formal compositional model for concurrent stochastic timed systems, with general distributions and non-deterministic choices. Measures of interest are defined over schedulers that resolve the nondeterminism. In this paper we investigate the power of various theoretically and practically motivated classes of schedulers, considering the classic complete-information view and a restriction to non-prophetic schedulers. We prove a hierarchy of scheduler classes w.r.t. unbounded probabilistic reachability. We find that, unlike Markovian formalisms, stochastic automata distinguish most classes even in this basic setting. Verification and strategy synthesis methods thus face a tradeoff between powerful and efficient classes. Using lightweight scheduler sampling, we explore this tradeoff and demonstrate the concept of a useful approximative verification technique for stochastic automata