A note on Gabor frames in finite dimensions

The purpose of this note is to present a proof of the existence of Gabor frames in general linear position in all finite dimensions. The tools developed in this note are also helpful towards an explicit construction of such a frame, which is carried out in the last section. This result has applications in signal recovery through erasure channels, operator identification, and time-frequency analysis.Comment: 10 page

Soil and crop responses following application of biosolids-derived organomineral fertilisers to ryegrass (Lolium perenne L.) grown in pots

Biosolids-derived organomineral fertilisers (OMF) were produced using a novel technique reported in earlier studies. This technique enables addition of N and potash to biosolids granules to form a balanced NPK fertiliser. Two fertiliser products; OMF10 (10:4:4) and OMF15 (15:4:4), were formulated and tested in a glasshouse facility on pot-grown ryegrass in comparison with urea and biosolids granules at N application rates ranging from 0 to 300 kg ha-1. The aim of this research was to contribute to the understanding of nutrients management and dynamics in grass crops fertilised with OMF. The study focused upon dry matter yield (DMY) and crop responses to applied fertiliser, nitrogen use efficiency (NUE) and fertilisers’ effect on soil fertility. Results indicated that ryegrass responds linearly to application of OMF increasing DMY by about 2% to 27% compared with biosolids but to a lesser extent than urea (range: 17% to 55%). NUE was related to the concentration of readily available N in the fertiliser; urea and OMF showed significantly greater (P<0.05) N recoveries than biosolids (26% to 75%, and 19% to 29%, respectively). Total nitrogen in soil and SOM increased (P<0.05) depending on the concentration of organic-N in the fertiliser applied. DMY was lower but more sustained overtime in biosolids-treated pots. OMF application did not result in significant changes in soil extractable-P levels whereas for urea, it decreased significantly while it showed a significant increase in biosolids-treated pots, where soil-P Index changed from 5 to 6. In OMF-treated soil, soil P Index remained close to constant overtime thereby supporting the purpose of the formulations tested

Discrete squeezed states for finite-dimensional spaces

We show how discrete squeezed states in an $N^{2}$-dimensional phase space can be properly constructed out of the finite-dimensional context. Such discrete extensions are then applied to the framework of quantum tomography and quantum information theory with the aim of establishing an initial study on the interference effects between discrete variables in a finite phase-space. Moreover, the interpretation of the squeezing effects is seen to be direct in the present approach, and has some potential applications in different branches of physics.Comment: 16 pages; 3 figure

Spark deficient Gabor frames

The theory of Gabor frames of functions defined on finite abelian groups was initially developed in order to better understand the properties of Gabor frames of functions defined over the reals. However, during the last twenty years the topic has acquired an interest of its own. One of the fundamental questions asked in this finite setting is the existence of full spark Gabor frames. The author proved the existence, as well as constructed such frames, when the underlying group is finite cyclic. In this paper, we resolve the non-cyclic case; in particular, we show that there can be no full spark Gabor frames of windows defined on finite abelian non-cyclic groups. We also prove that all eigenvectors of certain unitary matrices in the Clifford group in odd dimensions generate spark deficient Gabor frames. Finally, similarities between the uncertainty principles concerning the finite dimensional Fourier transform and the short-time Fourier transform are discussed.Comment: 16 pages. Incorporated referee's remarks. To appear in the Pacific Journal of Mathematic

Prioritized Garbage Collection: Explicit GC Support for Software Caches

Programmers routinely trade space for time to increase performance, often in the form of caching or memoization. In managed languages like Java or JavaScript, however, this space-time tradeoff is complex. Using more space translates into higher garbage collection costs, especially at the limit of available memory. Existing runtime systems provide limited support for space-sensitive algorithms, forcing programmers into difficult and often brittle choices about provisioning. This paper presents prioritized garbage collection, a cooperative programming language and runtime solution to this problem. Prioritized GC provides an interface similar to soft references, called priority references, which identify objects that the collector can reclaim eagerly if necessary. The key difference is an API for defining the policy that governs when priority references are cleared and in what order. Application code specifies a priority value for each reference and a target memory bound. The collector reclaims references, lowest priority first, until the total memory footprint of the cache fits within the bound. We use this API to implement a space-aware least-recently-used (LRU) cache, called a Sache, that is a drop-in replacement for existing caches, such as Google's Guava library. The garbage collector automatically grows and shrinks the Sache in response to available memory and workload with minimal provisioning information from the programmer. Using a Sache, it is almost impossible for an application to experience a memory leak, memory pressure, or an out-of-memory crash caused by software caching.Comment: to appear in OOPSLA 201

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Las clases particulares, un fraude

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