525 research outputs found
High-entropy dual functions over finite fields and locally decodable codes
No full textWe show that for infinitely many primes p, there exist dual functions of order k over Fnp that cannot be approximated in L∞-distance by polynomial phase functions of degree k−1. This answers in the negative a natural finite-field analog of a problem of Frantzikinakis on L∞-approximations of dual functions over N (a.k.a. multiple correlation sequences) by nilsequences
Quasirandomness in quantum information theory
No full textWe study quasirandomness in several contexts in quantum information theory. Roughly speaking, an object is quasirandom if it shares properties with a random object. What these properties are, depends on the context.Consider, for example, uniformly random 3-regular graphs. They have the property that they are likely highly connected, while at the same time the number of edges is quite small (the graph is “sparse”). Highly connected refers to the property that, for example, a random walk on the graph mixes very rapidly: after a small number of steps, the position of the walker is close to uniformly random. So when an explicit 3-regular graph has this property as well, we say that it is quasirandom.Among other things, interesting objects whose quasirandomness we study in this dissertation are linear maps from matrices to matrices or complex-valued functions on a finite abelian group. These objects appear in quantum information theory in the form of quantum channels or the amplitudes of quantum states for example.For quantum channels, we study the equivalence of certain quasirandom properties: we generalize the theory of quasirandom graphs to quantum information theory showing that “expansion” and “uniformity” are equivalent for very symmetric quantum channels.For quantum states we consider the notion of rank, where you want to express a quantum state in terms of a minimal number of simpler states called stabilizer states, this is the stabilizer rank. In this case, random quantum states have “high” stabilizer rank and we want to know if an explicit quantum state, say the magic state, has high stabilizer rank. Here we shed light on this problem by looking at this problem from a different perspective, through the lens of higher-order Fourier analysis
Is isotropy restored at small scales in freely decaying strongly stratified turbulence?
No full textWe analyse the scale-dependent anisotropy of homogeneous stratified turbulence. The Ozmidov scale l_N (Ozmidov 1965) helps to compare the relative effects of inertia and of the buoyancy force, and thus to quantify the rise of anisotropy in different scale ranges: at large scales l >> l_N the anisotropy due to strong stratification is dominant, whereas at small scales l << l_N, universal 3D isotropic characteristic of turbulence appear to be restored. We investigate the corresponding dynamics using Direct Numerical Simulations (DNS) in freely decaying turbulence at different stratification rates. We confirm the return to isotropy of the small scales by analyzing the orientation-dependent power spectrum and poloidal/toroidal/density energy modes. To some extent, many characteristics of isotropic universality are restored at small scales but, surprisingly, the density spectrum (also potential energy spectrum) plays a particular role
Quasirandom Quantum Channels
No full textMixing (or quasirandom) properties of the natural transition matrix associated to a graph can be quantified by its distance to the complete graph. Different mixing properties correspond to different norms to measure this distance. For dense graphs, two such properties known as spectral expansion and uniformity were shown to be equivalent in seminal 1989 work of Chung, Graham and Wilson. Recently, Conlon and Zhao extended this equivalence to the case of sparse vertex transitive graphs using the famous Grothendieck inequality.
Here we generalize these results to the non-commutative, or "quantum", case, where a transition matrix becomes a quantum channel. In particular, we show that for irreducibly covariant quantum channels, expansion is equivalent to a natural analog of uniformity for graphs, generalizing the result of Conlon and Zhao. Moreover, we show that in these results, the non-commutative and commutative (resp.) Grothendieck inequalities yield the best-possible constants
Quasirandomness in quantum information theory
No full textWe study quasirandomness in several contexts in quantum information theory. Roughly speaking, an object is quasirandom if it shares properties with a random object. What these properties are, depends on the context.Consider, for example, uniformly random 3-regular graphs. They have the property that they are likely highly connected, while at the same time the number of edges is quite small (the graph is “sparse”). Highly connected refers to the property that, for example, a random walk on the graph mixes very rapidly: after a small number of steps, the position of the walker is close to uniformly random. So when an explicit 3-regular graph has this property as well, we say that it is quasirandom.Among other things, interesting objects whose quasirandomness we study in this dissertation are linear maps from matrices to matrices or complex-valued functions on a finite abelian group. These objects appear in quantum information theory in the form of quantum channels or the amplitudes of quantum states for example.For quantum channels, we study the equivalence of certain quasirandom properties: we generalize the theory of quasirandom graphs to quantum information theory showing that “expansion” and “uniformity” are equivalent for very symmetric quantum channels.For quantum states we consider the notion of rank, where you want to express a quantum state in terms of a minimal number of simpler states called stabilizer states, this is the stabilizer rank. In this case, random quantum states have “high” stabilizer rank and we want to know if an explicit quantum state, say the magic state, has high stabilizer rank. Here we shed light on this problem by looking at this problem from a different perspective, through the lens of higher-order Fourier analysis
The tautological ring of Mg,n via Pandharipande-Pixton-Zvonkine r-spin relations
No full textWe use relations in the tautological ring of the moduli spaces Mg,n derived by Pandharipande, Pixton, and Zvonkine from the Givental formula for the r-spin Witten class in order to obtain some restrictions on the dimensions of the tautological rings of the open moduli spacesMg,n. In particular, we give a new proof for the result of Looijenga (for n = 1) and Buryak et al. (for n > 2) that dimRg-1(Mg,n) ≤ n. We also give a new proof of the result of Looijenga (for n = 1) and Ionel (for arbitrary n > 1) that Ri(Mg,n) = 0 for i > g and give some estimates for the dimension of Ri(Mg,n) for i ≤ g - 2
Automation in sensing and raw material characterization - A conceptual framework
No full textThe use of sensor technologies for material characterization is rapidly growing and innovative advancement is observed. However, the use of sensor combinations for a raw material characterization in mining is very limited and automation of the material identification process using a combined sensor signal is not defined. Potential sensor technologies for raw material characterization were evaluated based on the applicability and technological maturity. To ensure a rapid implementation of the Real-time mining (RTM) project concept, mature technologies such as Red Green Blue (RGB) imaging, Visible Near Infrared (VNIR) hyperspectral imaging, Short Wave Infrared (SWIR) hyperspectral imaging, Fourier-Transform Infrared Spectroscopy (FTIR), Laser Induced Breakdown Spectroscopy (LIBS) and Raman were selected. Each selected technology was assessed for automation in sensing and applicability (for characterization of the test case materials). Based on the results the sensor data were further considered for data fusion. The proposed sensor combinations approach encompasses three levels of data fusion: low-level, mid-level and high-level. The data of the different sensors are fused together in order to acquire a wide range of mineral properties within each lithotype and an improved classification and predictive models. The preferred level of data fusion and preferred sensor data combinations will be used to develop a multi-variate statistical interpretation rule which relates combination of sensors signals with raw material properties. Thus a tool which integrates the combined sensor signal with materials properties will be developed and used to automate the material characterization process.Accepted Author ManuscriptResource Engineerin
Experimental and computational study of the influence of pre-damage patterns in unreinforced masonry crack propagation due to induced, repeated earthquakes
No full textInduced seismicity in the north of the Netherlands has recently exposed unprepared, unreinforced masonry structures to considerable earthquake risk. While the ultimate-limit state capacity of the structures is vital to assess the individual’s risk, their behavior during more frequent, lighter earthquakes, leading to ‘lighter damage’, has shown to be strongly linked to economic losses and societal unrest. When observing the light damage caused by minor earthquakes, the existing state of the structure appears to be highly relevant for the final damage intensity and configuration: earthquakes that may have otherwise caused no apparent damage, may intensify existing damage. In particular, incipient damage due to settlements is common in the baked-clay and calcium-silicate brick masonry structures of the region.This paper details the study of full-scale laboratory walls, pre-damaged following typical (crack) patterns caused by settlements and tested with quasi-static lateral loads. The aggravation of the damage during a relevant number of load cycles is monitored using full-field digital image correlation. The damage is quantified objectively using a purposely-developed damage parameter.The tests are used (together with previous studies) to further calibrate computational finite element models, which coupled with detailed soil-structure interaction boundary conditions, are then employed to assess a larger number of structural geometries and pre-damaged configurations exposed to (repeated) induced earthquake acceleration histories.Both experimental and computational approaches show that settlement pre-damage in masonry structures increases the likelihood and the amount of further damage. This is more easily observed when some initial, yet limited damage exists and the masonry wall is exposed to moderate earthquake vibrations in the order of 30 millimeters per second.Accepted Author ManuscriptApplied Mechanic
Re: An Institution Par Excellence: Prof. B. Ramamurthi 1922-2003. Surg Neurol 2004;61:511-14 [1]
No full text[No abstract available]0
Sensing and data fusion opportunities for raw material characterisation in mining: Technology and data-driven approach
No full textThe rising demands for mined products lead to the extraction of materials in geologically complex regions. This calls for mining process changes and interventions driven by technology and advanced data analytics. The dynamic development of state-of-the-art sensor technologies and their potential use in mining is projected to significantly reduce costs in the industry. However, despite rapid advances in sensor technologies, there is still a demand for novel data analytical approaches to enable accurate characterisation of material along the mining value chain, as advanced data analytics is key to gain knowledge from the complex sensor-derived data. Therefore, sensor technology, coupled with advanced data analytics is crucial for the rapid and accurate characterisation of material in mining operations. Access to rapid and accurate data on the key geological attributes (e.g., mineralogy and geochemistry) along the mining value chain has significant implications for the production process efficiency in commercial mines. Such data would greatly assist the improvement of deposit models, optimise ore processing, specify product quality and improve operational decision-making. Sensor technologies operate over a specific range of the electromagnetic spectrum and provide information on certain aspects of material properties that are of potential interest for mining extraction. However, a single sensor might not provide a sufficiently comprehensive description of a material’s composition. This introduces uncertainty into both resource estimation and requirements definition for mineral processing. Thus, it is necessary to utilise strategic sensor combinations to improve accuracy, minimise uncertainty, and enhance specific insights of material compositions. Combinations of sensors can be implemented using a data fusion approach. The fusion of sensed data can be realised at different levels: low-, mid-, and high-level, when the integration occurs at the data level, features level and decision level, respectively. This research aims to develop methods for the characterisation of raw materials using multiple sensor technologies and sensor combinations concept (data fusion at different levels), that can be potentially applicable to mining operations. The study involved the multispectral and hyperspectral imaging techniques, such as red-green-blue (RGB) imaging, visible and near-infrared (VNIR) and short-wave infrared (SWIR) hyperspectral imaging, and point spectroscopic techniques, such as mid-wave infrared (MWIR), long-wave infrared (LWIR) and Raman spectroscopy to acquire spectral information over a wider range of the electromagnetic spectrum. First, an investigation was conducted on the usability of the individual sensor technologies coupled with data analytics for the characterisation of a polymetallic sulphide deposit at different levels. The different levels of material characterisation aimed to allow mineral mapping, ore–waste discrimination, fragmentation analysis, and semi-quantitative analysis of elements and minerals. The positive outcomes of the use of the individual techniques led to the development of a data fusion framework that enables data integration (including multi-scale and multi-resolution data) at different levels (e.g., low-level and mid-level). The developed data fusion concept was implemented and validated using different test scenarios..
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