Some relations between Bohl Exponents and the Exponential Dichotomy spectrum

We study a liaison between the Bohl's exponents and the exponential dichotomy spectrum of a non autonomous linear system of difference equations on the whole line $\mathbb{Z}$. More specifically, We prove that for any initial condition in an invariant vector bundle, associated to its exponential dichotomy spectrum, its Bohl's exponents are contained in an spectral interval.Comment: 9 page

The Neural Representation Benchmark and its Evaluation on Brain and Machine

A key requirement for the development of effective learning representations is their evaluation and comparison to representations we know to be effective. In natural sensory domains, the community has viewed the brain as a source of inspiration and as an implicit benchmark for success. However, it has not been possible to directly test representational learning algorithms directly against the representations contained in neural systems. Here, we propose a new benchmark for visual representations on which we have directly tested the neural representation in multiple visual cortical areas in macaque (utilizing data from [Majaj et al., 2012]), and on which any computer vision algorithm that produces a feature space can be tested. The benchmark measures the effectiveness of the neural or machine representation by computing the classification loss on the ordered eigendecomposition of a kernel matrix [Montavon et al., 2011]. In our analysis we find that the neural representation in visual area IT is superior to visual area V4. In our analysis of representational learning algorithms, we find that three-layer models approach the representational performance of V4 and the algorithm in [Le et al., 2012] surpasses the performance of V4. Impressively, we find that a recent supervised algorithm [Krizhevsky et al., 2012] achieves performance comparable to that of IT for an intermediate level of image variation difficulty, and surpasses IT at a higher difficulty level. We believe this result represents a major milestone: it is the first learning algorithm we have found that exceeds our current estimate of IT representation performance. We hope that this benchmark will assist the community in matching the representational performance of visual cortex and will serve as an initial rallying point for further correspondence between representations derived in brains and machines.Comment: The v1 version contained incorrectly computed kernel analysis curves and KA-AUC values for V4, IT, and the HT-L3 models. They have been corrected in this versio

Comparing state-of-the-art visual features on invariant object recognition tasks

Tolerance (“invariance”) to identity-preserving image variation (e.g. variation in position, scale, pose, illumination) is a fundamental problem that any visual object recognition system, biological or engineered, must solve. While standard natural image database benchmarks are useful for guiding progress in computer vision, they can fail to probe the ability of a recognition system to solve the invariance problem. Thus, to understand which computational approaches are making progress on solving the invariance problem, we compared and contrasted a variety of state-of-the-art visual representations using synthetic recognition tasks designed to systematically probe invariance. We successfully re-implemented a variety of state-of-the-art visual representations and confirmed their published performance on a natural image benchmark. We here report that most of these representations perform poorly on invariant recognition, but that one representation shows significant performance gains over two baseline representations. We also show how this approach can more deeply illuminate the strengths and weaknesses of different visual representations and thus guide progress on invariant object recognition

PyCUDA and PyOpenCL: A Scripting-Based Approach to GPU Run-Time Code Generation

High-performance computing has recently seen a surge of interest in heterogeneous systems, with an emphasis on modern Graphics Processing Units (GPUs). These devices offer tremendous potential for performance and efficiency in important large-scale applications of computational science. However, exploiting this potential can be challenging, as one must adapt to the specialized and rapidly evolving computing environment currently exhibited by GPUs. One way of addressing this challenge is to embrace better techniques and develop tools tailored to their needs. This article presents one simple technique, GPU run-time code generation (RTCG), along with PyCUDA and PyOpenCL, two open-source toolkits that support this technique. In introducing PyCUDA and PyOpenCL, this article proposes the combination of a dynamic, high-level scripting language with the massive performance of a GPU as a compelling two-tiered computing platform, potentially offering significant performance and productivity advantages over conventional single-tier, static systems. The concept of RTCG is simple and easily implemented using existing, robust infrastructure. Nonetheless it is powerful enough to support (and encourage) the creation of custom application-specific tools by its users. The premise of the paper is illustrated by a wide range of examples where the technique has been applied with considerable success.Comment: Submitted to Parallel Computing, Elsevie

Deep Neural Networks Rival the Representation of Primate IT Cortex for Core Visual Object Recognition

The primate visual system achieves remarkable visual object recognition performance even in brief presentations and under changes to object exemplar, geometric transformations, and background variation (a.k.a. core visual object recognition). This remarkable performance is mediated by the representation formed in inferior temporal (IT) cortex. In parallel, recent advances in machine learning have led to ever higher performing models of object recognition using artificial deep neural networks (DNNs). It remains unclear, however, whether the representational performance of DNNs rivals that of the brain. To accurately produce such a comparison, a major difficulty has been a unifying metric that accounts for experimental limitations such as the amount of noise, the number of neural recording sites, and the number trials, and computational limitations such as the complexity of the decoding classifier and the number of classifier training examples. In this work we perform a direct comparison that corrects for these experimental limitations and computational considerations. As part of our methodology, we propose an extension of "kernel analysis" that measures the generalization accuracy as a function of representational complexity. Our evaluations show that, unlike previous bio-inspired models, the latest DNNs rival the representational performance of IT cortex on this visual object recognition task. Furthermore, we show that models that perform well on measures of representational performance also perform well on measures of representational similarity to IT and on measures of predicting individual IT multi-unit responses. Whether these DNNs rely on computational mechanisms similar to the primate visual system is yet to be determined, but, unlike all previous bio-inspired models, that possibility cannot be ruled out merely on representational performance grounds.Comment: 35 pages, 12 figures, extends and expands upon arXiv:1301.353

The economics of desertification, land degradation, and drought: Toward an integrated global assessment

cost of inaction, desertification, drought, Economics, Land degradation, prevention of land degradation,

The Economics of Desertification, Land Degradation, and Drought; Toward an Integrated Global Assessment

Land degradation has not been comprehensively addressed at the global level or in developing countries. A suitable economic framework that could guide investments and institutional action is lacking. This study aims to overcome this deficiency and to provide a framework for a global assessment based on a consideration of the costs of action versus inaction regarding desertification, land degradation, and drought (DLDD). Most of the studies on the costs of land degradation (mainly limited to soil erosion) give cost estimates of less than 1 percent up to about 10 percent of the agricultural gross domestic product (GDP) for various countries worldwide. But the indirect costs of DLDD on the economy (national income), as well as their socioeconomic consequences (particularly poverty impacts), must be accounted for, too. Despite the numerous challenges, a global assessment of the costs of action and inaction against DLDD is possible, urgent, and necessary. This study provides a framework for such a global assessment and provides insights from some related country studies.Agricultural Finance, Crop Production/Industries, Environmental Economics and Policy, Land Economics/Use, Resource /Energy Economics and Policy,

Why is Real-World Visual Object Recognition Hard?

Progress in understanding the brain mechanisms underlying vision requires the construction of computational models that not only emulate the brain's anatomy and physiology, but ultimately match its performance on visual tasks. In recent years, “natural” images have become popular in the study of vision and have been used to show apparently impressive progress in building such models. Here, we challenge the use of uncontrolled “natural” images in guiding that progress. In particular, we show that a simple V1-like model—a neuroscientist's “null” model, which should perform poorly at real-world visual object recognition tasks—outperforms state-of-the-art object recognition systems (biologically inspired and otherwise) on a standard, ostensibly natural image recognition test. As a counterpoint, we designed a “simpler” recognition test to better span the real-world variation in object pose, position, and scale, and we show that this test correctly exposes the inadequacy of the V1-like model. Taken together, these results demonstrate that tests based on uncontrolled natural images can be seriously misleading, potentially guiding progress in the wrong direction. Instead, we reexamine what it means for images to be natural and argue for a renewed focus on the core problem of object recognition—real-world image variation