Acoustic and Large Eddy Simulation studies of azimuthal modes in annular combustion chambers

The objectives of this paper are the description of azimuthal instability modes found in annular combus- tion chambers using two numerical tools: (1) Large Eddy Simulation (LES) methods and (2) acoustic solv- ers. These strong combustion instabilities are difficult to study experimentally and the present study is based on a LES of a full aeronautical combustion chamber. The LES exhibits a self-excited oscillation at the frequency of the first azimuthal eigenmode. The mesh independence of the LES is verified before ana- lysing the nature of this mode using various indicators over more than 100 cycles: the mode is mostly a pure standing mode but it transitions from time to time to a turning mode because of turbulent fluctu- ations, confirming experimental observations and theoretical results. The correlation between pressure and heat release fluctuations (Rayleigh criterion) is not verified locally but it is satisfied when pressure and heat release are averaged over sectors. LES is also used to check modes predicted by an acoustic Helmholtz solver where the flow is frozen and flames are modelled using a Flame Transfer Function (FTF) as done in most present tools. The results in terms of mode structure compare well confirming that the mode appearing in the LES is the first azimuthal mode of the chamber. Moreover, the acoustic solver provides stability maps suggesting that a reduction of the time delay of the FTF would be enough to sta- bilise the mode. This is confirmed with LES by increasing the flame speed and verifying that this modi- fication leads to a damped mode in a few cycles

Coordinated optimization of visual cortical maps : 2. Numerical studies

In the juvenile brain, the synaptic architecture of the visual cortex remains in a state of flux for months after the natural onset of vision and the initial emergence of feature selectivity in visual cortical neurons. It is an attractive hypothesis that visual cortical architecture is shaped during this extended period of juvenile plasticity by the coordinated optimization of multiple visual cortical maps such as orientation preference (OP), ocular dominance (OD), spatial frequency, or direction preference. In part (I) of this study we introduced a class of analytically tractable coordinated optimization models and solved representative examples, in which a spatially complex organization of the OP map is induced by interactions between the maps. We found that these solutions near symmetry breaking threshold predict a highly ordered map layout. Here we examine the time course of the convergence towards attractor states and optima of these models. In particular, we determine the timescales on which map optimization takes place and how these timescales can be compared to those of visual cortical development and plasticity. We also assess whether our models exhibit biologically more realistic, spatially irregular solutions at a finite distance from threshold, when the spatial periodicities of the two maps are detuned and when considering more than 2 feature dimensions. We show that, although maps typically undergo substantial rearrangement, no other solutions than pinwheel crystals and stripes dominate in the emerging layouts. Pinwheel crystallization takes place on a rather short timescale and can also occur for detuned wavelengths of different maps. Our numerical results thus support the view that neither minimal energy states nor intermediate transient states of our coordinated optimization models successfully explain the architecture of the visual cortex. We discuss several alternative scenarios that may improve the agreement between model solutions and biological observations

Coordinated optimization of visual cortical maps : 1. Symmetry-based analysis

In the primary visual cortex of primates and carnivores, functional architecture can be characterized by maps of various stimulus features such as orientation preference (OP), ocular dominance (OD), and spatial frequency. It is a long-standing question in theoretical neuroscience whether the observed maps should be interpreted as optima of a specific energy functional that summarizes the design principles of cortical functional architecture. A rigorous evaluation of this optimization hypothesis is particularly demanded by recent evidence that the functional architecture of orientation columns precisely follows species invariant quantitative laws. Because it would be desirable to infer the form of such an optimization principle from the biological data, the optimization approach to explain cortical functional architecture raises the following questions: i) What are the genuine ground states of candidate energy functionals and how can they be calculated with precision and rigor? ii) How do differences in candidate optimization principles impact on the predicted map structure and conversely what can be learned about a hypothetical underlying optimization principle from observations on map structure? iii) Is there a way to analyze the coordinated organization of cortical maps predicted by optimization principles in general? To answer these questions we developed a general dynamical systems approach to the combined optimization of visual cortical maps of OP and another scalar feature such as OD or spatial frequency preference. From basic symmetry assumptions we obtain a comprehensive phenomenological classification of possible inter-map coupling energies and examine representative examples. We show that each individual coupling energy leads to a different class of OP solutions with different correlations among the maps such that inferences about the optimization principle from map layout appear viable. We systematically assess whether quantitative laws resembling experimental observations can result from the coordinated optimization of orientation columns with other feature maps

Solar farm cable layout optimization as a graph problem

We introduce the Solar Farm Cable Layout Problem (SoFaCLaP), a novel graph-theoretic optimization problem. SoFaCLaP formalizes the task of finding a cost-optimal cable layout in a solar farm where PV string positions are already determined but the positions of other components such as transformers can be picked from a set of candidate positions. The problem statement incorporates a network flow model in which the flow value of a connection represents the number of strings that are (indirectly) connected to a transformer via this connection. A mixed-integer linear program (MILP) formulation is proposed that uses binary variables to indicate which of several available cable types is chosen for each connection. We propose a framework to randomly generate benchmark instances to evaluate any algorithmic approach to SoFaCLaP. In particular, we generate a set of instances based on real-world solar farm characteristics. With an extensive evaluation of the MILP formulation on those instances we establish mixed-integer linear programming as a baseline for future algorithmic approaches to finding solar farm cable layouts

Sensitivity analysis of AI-based algorithms for autonomous driving on optical wavefront aberrations induced by the windshield

Autonomous driving perception techniques are typically based on supervised machine learning models that are trained on real-world street data. A typical training process involves capturing images with a single car model and windshield configuration. However, deploying these trained models on different car types can lead to a domain shift, which can potentially hurt the neural networks performance and violate working ADAS requirements. To address this issue, this paper investigates the domain shift problem further by evaluating the sensitivity of two perception models to different windshield configurations. This is done by evaluating the dependencies between neural network benchmark metrics and optical merit functions by applying a Fourier optics based threat model. Our results show that there is a performance gap introduced by windshields and existing optical metrics used for posing requirements might not be sufficient

Regulated Parsing

Tato práce se zabývá rozšířenými modely bezkontextových gramatik a zkoumá možnosti jejich úpravy a využití pro deterministickou syntaktickou analýzu pomocí metod hluboké syntaktické analýzy struktur, které nejsou bezkontextové. Zavádí upravený bezkontextový model LL programovaných gramatik a hlubokého zásobníkového automatu, umožňující deterministickou syntaktickou analýzu těchto struktur.This work deals with advanced models of context-free grammars and explores the possibilities of adaptation and usefulness for deterministic parsing of non-context-free sructures by deep parsing method. It introduces adapted model of context-free grammar named LL programmed grammar and adapted deep pushdown automaton that makes deterministic parsing of non-context-free structures possible.

Windscreen Optical Quality for AI Algorithms: Refractive Power and MTF not Sufficient

Windscreen optical quality is an important aspect of any advanced driver assistance system, and also for future autonomous driving, as today at least some cameras of the sensor suite are situated behind the windscreen. Automotive mass production processes require measurement systems that characterize the optical quality of the windscreens in a meaningful way, which for modern perception stacks implies meaningful for artificial intelligence (AI) algorithms. The measured optical quality needs to be linked to the performance of these algorithms, such that performance limits - and thus production tolerance limits - can be defined. In this article we demonstrate that the main metric established in the industry - refractive power - is fundamentally not capable of capturing relevant optical properties of windscreens. Further, as the industry is moving towards the modulation transfer function (MTF) as an alternative, we mathematically show that this metric cannot be used on windscreens alone, but that the windscreen forms a novel optical system together with the optics of the camera system. Hence, the required goal of a qualification system that is installed at the windscreen supplier and independently measures the optical quality cannot be achieved using MTF. We propose a novel concept to determine the optical quality of windscreens and to use simulation to link this optical quality to the performance of AI algorithms, which can hopefully lead to novel inspection systems

A variational perspective on auxetic metamaterials of checkerboard-type

The main result of this work is a homogenization theorem via variational convergence for elastic materials with stiff checkerboard-type heterogeneities under the assumptions of physical growth and non-self-interpenetration. While the obtained energy estimates are rather standard, determining the effective deformation behavior, or in other words, characterizing the weak Sobolev limits of deformation maps whose gradients are locally close to rotations on the stiff components, is the challenging part. To this end, we establish an asymptotic rigidity result, showing that, under suitable scaling assumptions, the attainable macroscopic deformations are affine conformal contractions. This identifies the composite as a mechanical metamaterial with a negative Poisson's ratio. Our proof strategy is to tackle first an idealized model with full rigidity on the stiff tiles to acquire insight into the mechanics of the model and then transfer the findings and methodology to the model with diverging elastic constants. The latter requires, in particular, a new quantitative geometric rigidity estimate for non-connected squares touching each other at their vertices and a tailored Poincar\'e type inequality for checkerboard structures.Comment: 40 pages, 13 figure