Visual object concept discovery: Observations in congenitally blind children, and a computational approach Over the course of the first few months of life, our brains accomplish a remarkable feat. They are able to interpret complex visual images so that instead of being just disconnected collections of colors and textures, they become meaningful sets of distinct objects. Exactly how this is accomplished is poorly understood. We approach this problem from both experimental and computational perspectives. On the experimental side, we have launched a new humanitarian and scientific initiative in India, called 'Project Prakash'. This project involves a systematic study of the development of object-perception skills in children following recovery from congenital blindness. Here, we provide an overview of Project Prakash and also describe a specific study related to the development of faceperception skills following sight recovery. Based in part on the results of these experiments, we then develop a computational framework for addressing the problem of object concept discovery. Our model seeks to find repeated instances of a pattern in multiple training images. The source of complexity lies in the non-normalized nature of the inputs: the pattern is unconstrained in terms of where it can appear in the images, the background is complex and constitutes the overwhelming majority of the image, and the pattern can change significantly from one training instance to another. For the purpose of demonstration, we focus on human faces as the pattern of interest, and describe the sequence of steps through which the model is able to extract a face concept from non-normalized example images. Additionally, we test the model's robustness to degradations in the inputs. This is important to assess the model's congruence with developmental processes in human infancy, or following treatment for extended congenital blindness, when visual acuity is significantly compromised. r 2007 Published by Elsevier B.V. Through experience, the brain becomes adept at parsing complex visual scenes into distinct objects. An infant, for example, learns that certain constellations of visual cues correspond to her father. Later, when the relation has solidified, the child is capable of recognizing ''father'' quickly, and from a variety of viewpoints or illumination conditions. But how does a child, with no prior information, identify an object of interest across a collection of possibly ambiguous or cluttered images? Understanding how the human visual system learns to perceive objects in the environment is one of the fundamental challenges in neuroscience, and it is this question that motivates our work. We do not wish to take a dogmatic stand on whether the brain of an infant is a 'blank slate' or loaded with innate knowledge. What we do wish to investigate, however, is the computational feasibility of acquiring object concepts without presupposing the existence of innate representations.. The research presented in this paper comprises two complementary components: in the first half, we describe an experimental field study from ''Project Prakash.'' A new humanitarian and scientific initiative launched in India, Project Prakash involves a systematic study of the development of object-perception skills in children following recovery from congenital blindness. In the latter half of the paper, we introduce a computational model for visual object concept discovery. Through this computational investigation, we seek to illuminate from a different angle the process by which humans build object models. Constructing a machine analog of this process, however, is a difficult computational challenge given that natural images are often complex and contain many attributes irrelevant to the concept that needs to be extracted. Several issues concerning this process remain open: how much visual experience is needed for the development of this ability? What are the intermediate stages in the evolution of object representations? How does the quality of early visual input influence the development of object concepts? These questions are of central importance for both the children enrolled in Project Prakash and our computational system alike. In pursuing the latter, it is our goal to determine the nature of learning processes which individuals recovering from blindness might plausibly use to discover visual object concepts. We have provided an overview of some of our experimental studies and computational modeling efforts that have the goal of investigating object concept learning. The experimental studies have some obvious limitations, the most significant being the small number of test subjects. Taken just by themselves, the experimental results included here are suggestive rather than definitive. However, we believe that there is reason to expect these findings to generalize. The high consistency between results from SB and KK, and also similar observations in ongoing studies with other subjects in Project Prakash suggest that the pattern of results reported here might hold more generally.. It is worth emphasizing that the current experimental data are not extensive enough to suggest very specific computational strategies for a modeling effort. However, they do provide some broad constraints for a model's design, and simultaneously rule out certain classes of models, such as those dependent critically on the use of fine-grained luminance edge-information. They indicate the potential importance of cues such as color, and the sufficiency of low-resolution image information. The model we have proposed cannot yet be said to faithfully reflect the object learning strategies instantiated in the brain. But, in providing one possible approach, the model allows us to assess the plausibility of the general computational framework it embodies. The particular algorithmic decisions we have made in the model presented here (such as the use of K-means clustering or principal components analysis) are not driven by specific experimental results, but the overall structure of the model is intended to be consistent with empirical data.. Before considering the model's features, let us examine a few of its limitations. The training inputs it can handle at present cannot be entirely unconstrained. While we have placed no restrictions on the location of the target object or the complexity of the background, we have sidestepped the challenges of size, pose and orientation variability by fixing these parameters. We have also not so far devised a completely principled way of selecting patch sizes for the initial analysis of inputs. Furthermore, our representation strategy could be augmented with additional biologically plausible image features/measurements to yield improved clustering performance. However, despite these limitations, we believe that this computational system suggests one plausible model for object concept learning in infants and individuals recovering from blindness. The model has begun serving a useful purpose for demonstrating feasibility of explanations regarding experimental data by mimicking some aspects of human performance. We explore some of these parallels next.. The model's reliable performance at a resolution approximating that of infants and Project Prakash participants, implies that, at least in principle, concept discovery is possible with significantly impaired acuity and some sensory assistance to provide implicit labels, which constitute a weak form of supervision. Future development of the model presents the opportunity to provide concept realization without labels of any sort, thus providing a computational analog to object concept learning in humans given static scenes and zero additional sensory input. Beginnings have already been made in this direction. For instance, recent work by Fei-Fei et al. [8] has explored concept discovery when supervisory input is eliminated entirely.. It should be noted that of the cues available to both children during early development [4, 13] and the computational system, color information plays a significant role. In infants, color contributes strongly to orientation and segmentation of objects for eventual identification and recognition, and this is especially true in the absence of motion or other peripheral cues (as in static images). Correspondingly, double-opponency color filters are an integral part of the saliency computation we apply to the dataset of images in the computational model.. It is also interesting to consider the congruence between the computational model and the experimental results from

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Lattices that admit logarithmic worst-case to average-case connection factors We exhibit an average-case problem that is as hard as finding γ(n)-approximate shortest nonzero vectors in certain ndimensional lattices in the worst case, for γ(n) = O( √ log n). The previously best known factor for any non-trivial class of lattices was γ(n) =Õ(n).Our results apply to families of lattices having special algebraic structure. Specifically, we consider lattices that correspond to ideals in the ring of integers of an algebraic number field. The worst-case problem we rely on is to find approximate shortest vectors in these lattices, under an appropriate form of preprocessing of the number field.For the connection factors γ(n) we achieve, the corresponding decision problems on ideal lattices are not known to be NP-hard; in fact, they are in P. However, the search approximation problems still appear to be very hard. Indeed, ideal lattices are well-studied objects in computational number theory, and the best known algorithms for them seem to perform no better than the best known algorithms for general lattices.To obtain the best possible connection factor, we instantiate our constructions with infinite families of number fields having constant root discriminant. Such families are known to exist and are computable, though no efficient construction is yet known. Our work motivates the search for such constructions. Even constructions of number fields having root discriminant up to O(n 2/3− ) would yield connection factors better thanÕ(n).As an additional contribution, we give reductions between various worst-case problems on ideal lattices, showing for example that the shortest vector problem is no harder than the closest vector problem. These results are analogous to previously-known reductions for general lattices. In 1996, Ajtai established a remarkable connection between the worst-case and average-case complexity of certain computational problems on lattices [2] . He showed that approximating the length of the shortest nonzero vector in ndimensional lattices to within a certain connection factor γ(n) = poly(n) in the worst case reduces to solving a related problem on the average. This result opened the door to basing cryptography on a worst-case assumption, namely, that no efficient algorithm can approximately solve the shortest vector problem (SVP) to within a γ(n) factor on every lattice of dimension n.. It seems reasonable to assume that SVP is indeed hard. The problem dates back over 150 years, and it has been heavily scrutinized ever since. A major breakthrough occurred in 1982, when Lenstra, Lenstra, and Lovász designed an efficient algorithm that approximates SVP to within a 2 O(n) factor [29] (which was later improved to 2 The most important open problem, in our view, is the explicit construction of families of number fields having small root discriminant. Such constructions would also have applications in coding theory [30, 23] . It would be even nicer to find an explicit construction which provides, by design, the non-uniform advice needed by our reductions.. In contrast to prior work on average-case hardness from lattice problems (e.g., [2, 21, 36, 40, 31] ), we do not yet know how to obtain cryptographic hardness (e.g. collisionresistant hash functions) from ideal lattices over an arbitrary good number field K. The reason is that we seem to require an efficient injective mapping from function inputs (bit strings) to sufficiently short vectors z ∈ O m K . This appears to require additional advice about the number field.. For example, if we had an "almost-orthogonal" short basis for O m K , then it would be possible to produce elements of O m K that are short enough in 2 length, simply by summing up subsets of the basis vectors. This would suffice for cryp-tographic hardness, assuming SVP is hard on ideal lattices in some p norm, p ≤ 2.

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How do you define and measure research productivity? Productivity is the quintessential indicator of efficiency in any production system. It seems it has become a norm in bibliometrics to define research productivity as the number of publications per researcher, distinguishing it from impact. In this work we operationalize the economic concept of productivity for the specific context of research activity and show the limits of the commonly accepted definition. We propose then a measurable form of research productivity through the indicator "Fractional Scientific Strength (FSS)", in keeping with the microeconomic theory of production. We present the methodology for measure of FSS at various levels of analysis: individual, field, discipline, department, institution, region and nation. Finally, we compare the ranking lists of Italian universities by the two definitions of research productivity. In 2010, Opthof and Leydesdorff criticized the statistical normalization of the Leiden CWTS "crown indicator". A year later, bibliometricians from the CWTS group (Waltman et al. 2011) admitted that the "old crown indicator" was mathematically inconsistent and adopted the normalization method suggested by the above authors, leading to a "new crown indicator": the mean normalized citation score, or MNCS. A counter-reply from Leydesdorff and Opthof (2011) was not long in arriving: although agreeing with the new statistical normalization, they then further recommended using the mean rather than the median to field normalize citations.. In a parallel story, since the original introduction of the h-index in 2005 by physicist Jorge E. Hirsch, over 1,600 articles have been written illustrating its merits and defects and proposing one variant after another, to the extent even the most devoted historian of bibliometrics would despair of tracing them all.. But is it possible that these two research performance indicators really merited all this attention, or is it a case of "Much ado about nothing"? These particular indicators have only been the most popular among a myriad of others proposed over recent years by scholars and practitioners. While bibliometricians undoubtedly intended to provide useful indicators and ever more accurate and reliable methods, they have actually been the cause of increasing confusion. The proliferation of proposals has actually generated a type of disorientation among decision makers, no longer able to discriminate the pros and cons of the various indicators for planning an actual evaluation exercise. The proof of this is the increasing number of expert commissions and working groups at institutional, national and supranational levels, formed to deliberate and recommend on this indicator, that set of indicators, and this or that measure of performance. Performance ranking lists at national and international levels are published with media fanfare, influencing opinion and practical choices. The impression of the current authors is that these rankings of scientific performance, produced by "nonbibliometricians" (THE 2013; SJTU 2013; QS 2013; etc.) and even by bibliometricians (University of Leiden, SCImago, etc.) , are largely based on what can easily be counted rather than "what really counts". It is also our impression that the large part of the performance evaluation indicators proposed in the literature arise from a primarily mathematical school of thought. While knowledge in this area is fundamental in the methodology for application, our personal conviction is that research evaluation indicators must necessarily derive from economic theory. Since research activity is a production process, it should be analyzed from the perspective of microeconomic theory of production. Performance, or the ability to perform, should be evaluated with respect to the specific goals and objectives to be achieved. Because objectives may vary across research institutions and along time, recommending a sole indicator of performance would be inappropriate. However this does not justify the proliferation of hundreds of indicators, which while they may offer ease of calculation have little or no utility for policy or management decisions. A nation or research institution could aim to improve its average research productivity, or the rate of concentration of top articles or top scientists, or aim for a combination of these efforts in different weights. However we doubt that any government or research administrator could pursue any improvement that would be revealed through measurement by the MNCS, h-index or average number of publications per researcher. As a consequence, all the research evaluations based on these indicators and their relative rankings are at best of little or no value, and are otherwise actually dangerous, due to the distortions embedded in the information provided to the decision-makers. What is certain is that the objectives for research systems must be stated in measurable terms representing the desired outcome of production activity.. In this work we intend to provide an operative definition of the principal indicator of efficiency of any production unit, productivity. In the context of research organizations, bibliometricians have become accustomed to define research productivity as the number of publications per researcher, distinguishing it from impact, which they measure by citations. Honestly, we are not able to date back the scholar who first introduced the above definition, but already in 1926 Alfred J. Lotka used the number of publications in his milestone work (Lotka 1926) where he presented what it is now known as the Lotka's law or research productivity. Unfortunately, from an economic standpoint, and we remind that productivity is a concept born into the economic theory, such definition makes little sense. It would be acceptable only if all publications had the same value or impact, but that could not be further from the truth. The objective of this paper is to operationalize the concept of productivity for the specific context of research activity and propose a measurable form of productivity. We will then present an indicator, Fractional Scientific Strength (FSS), which in our view is thus far the best in approximating the measure of productivity. We will also illustrate the methodology for measuring FSS in the evaluation of performance at various levels of analysis: individual, field, discipline, department, institution, region and nation. Finally, we compare Italian university ranking lists by the two definitions of productivity: FSS and average number of publications per researcher. Until now, bibliometrics has proposed indicators and methods for measuring research performance that are largely inappropriate from a microeconomics perspective. The h-index and most of its variants, for example, inevitably ignore the impact of works with a number of citations below h and all citations above h of the h-core works. The h-index also fails to fieldnormalize citations, to account for the number of co-authors and their order in the byline, Last but not least, because of the different intensity of publications across fields, productivity rankings need to be carried out by field (Abramo and D'Angelo 2007) , when in reality there is a human tendency to compare h-indexes for researchers across different fields. Each one of the proposed h-variant indicators tackles one of the many drawbacks of the h-index while leaving the others unsolved, so none can be considered completely satisfactory.. The new crown indicator, on the other hand, measures the average standardized citations of a set of publications, which cannot provide any indication of unit productivity. In fact a research unit with double the MNCS value of another unit could actually have half the productivity, if the second unit produced four times as many publications. Whatever the CWTS research group (Waltman et al. 2012 ) might claim for them, the annual world university rankings by MNCS are not "performance" rankings -unless someone abnormally views performance as average impact of product, rather than impact per unit of cost. Applying the CWTS method, a unit that produces only one article with 10 citations has better performance than a unit producing 100, where each but one of these gets 10 citations and the last one gets nine citations. From a different standpoint, an organization may worsen its MNCS ranking if it produces an additional article whose normalized impact is below the previous MNCS value, which is a paradox. Further, the methodology reported for producing the ranking lists does not describe any weighting for co-authorship on the basis of byline order. Similar drawbacks are embedded is the SCImago Institutions Ranking by their main indicator, the Normalized Impact, measuring the ratio between the average scientific impact of an institution and the world average impact of publications of the same time frame, document type and subject area. We do not further consider any of the many annual world institutional rankings that are severely size dependent: the SJTU Shanghai Jiao Tong University, THE-Times Higher Education and QS Quacquarelli Symonds rankings, among others. These seem to represent skilled communications and marketing operations, with the actual rankings resulting more from improvisation than scientifically-reasoned indicators and methods. Gross attempts to compare the research productivity of nations can be found in the groundbreaking work by May (1997) . He measured the relative international standing of 15 countries in science, medicine and engineering, by their shares of ISI-indexed publications and citations. The USA invariably ranked at the top for such indicators in all scientific sectors In an attempt to separate the effect of size (labor and capital) from the effect of the quality of the production factors, he then ranked countries by citations per unit of spending. King (2004) updated May's original work to 2002, covering a 10-year period. The new study increased the number of nations analyzed (31), provided a longitudinal analysis over two five-year periods, added further indicators (top 1% highly cited articles; average citations per paper), provided for normalization of citations to the mean for each field, and took account of year of publication, thus providing aggregate measures of the overall research standing of each country. Outputs and outcomes were then normalized to inputs (researchers, expenditures, GDP). Such attempts to normalize outputs and outcomes to inputs, have dealt with the data at the aggregate level and have not been able to avoid the consequent distortions. In fact while most scholars now typically normalize the observed output and citation data, accounting for the field and year of publication, the data on input are not correspondingly divided according to the fields of allocation, since the practitioners lack data on the numbers of researchers and the expenditures per field in the individual countries under comparison. Pepe and Kurtz (2012) have proposed a productivity indicator for individuals, the research impact quotient, which has similarities with the FSS. It is the quotient of the square root of "total research impact" to the time of production. The total research impact normalizes external (non-self) citations by the number of co-authors of the cited paper and the number of bibliographic references of the citing paper. While the elimination of self-citations is an acceptable option, the normalization by the number of references of the citing papers is questionable and would deserve further investigation. For papers with cross-disciplinary impact in fact, the value of a citation is negatively related to the length of the reference lists. A citation by a publication in physics would value less than that by a paper in mathematics simply because the former's list of references is in general longer.. The great majority of the more popular bibliometric indicators and the rankings based on their use present two fundamental limits: lack of normalization of the output value to the input value, and absence of classification of scientists by field of research. Without normalization there cannot be any measure of productivity, which is the quintessential indicator of performance in any production unit; without providing field classification of scientists, the rankings of multi-field research units will inevitably be distorted, due to the different intensity of publication across fields. An immediate corollary is that it is impossible to correctly compare productivity at international levels. To date in fact there is no international standard for classification of scientists and, we are further unaware of any nations that classify their scientists by field at domestic level, apart from Italy. The commonly accepted definition of productivity, i.e. the number of publications per researcher, makes little sense, because publications have different values. We have proposed a proxy measure of productivity, FSS, which embeds both quantity and quality of production, and permits measurement at different organizational levels. Both the indicator and the related methods can certainly be improved, however they do make sense according to economic theory of production. Other indicators and related rankings, such as the simple number (or fractional counting) of publications per researcher, or the average normalized impact, cannot alone provide evaluation of performance -however they could assume meaning if associated with a true measure of productivity. In fact if a research unit achieves average levels of productivity this could result from both average number of publications and meaningful impact, but also from the opposite case of high numbers of publications and low impact. In this case, knowing the performance in terms of number of publications and average normalized impact would provide useful information on which aspect (quantity or impact) of scientific production to strengthen for betterment of production efficiency.. Aside from having an indicator of research unit productivity, the decision-maker could also find others useful, such as ones informing on unproductive researchers, on top researchers (10%, 5%, 1%, etc.), highly-cited publications, dispersion of performance within and between research units, etc.. For the large part of the objectives and contexts where evaluation of research performance is conducted, productivity is either the most important or the only indicator that should inform policy, strategy and operational decisions. We thus issue a two-fold call to the scholars in the subject: first, to focus their knowledge and skills on further refining the measurement of the FSS indicator in contexts of real use; second, to refrain from distribution of institutions' performance ranking lists based on invalid indicators, which could have negative consequences when used by policy-makers and research administrators.

O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O B O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Analysis of random sleep scheme for wireless sensor networks Abstract: Energy conserving design is the research focus to prolong the lifetime of wireless sensor networks. A simple and effective way to save energy is to place sensor nodes in sleep mode periodically. However, sleep mode corresponds to low power consumption as well as to reduced network capacity and increased latency. This paper develops an analytical framework to study the interaction between random sleep scheme and network performance. Our framework consists of the queueing model for sensor node and performance model for the whole network. We derived the network throughput, power consumption and packet delivery delay. Our analytical models shed light on the guidelines to design random sleep scheme and enable us to explore the trade-offs existing between sensor sleep/active dynamics and those performance measures. Recently, wireless sensor networks emerged from a wide variety of applications and systems with vastly varying requirements and characteristics. There is no standard or generic architecture for wireless sensor network to date. A de facto definition of a wireless sensor network has been established as an ad hoc multi-hop network which consists of large number tiny homogeneous sensor nodes that are resource-constrained, mostly immobile and randomly deployed in the area of interest [1] . Due to limited transmission range of sensor node, the sensory data are delivered to a processing center, called sink node, via multi-hop communication. Thus, each sensor node plays the dual roles of being a data originator and a data router.. The performances of a sensor network are measured in terms of lifetime, capacity and packet delay, which are determined by the dynamic behavior of sensor nodes, the efficiency of MAC protocol [2] - [7] , the routing protocol [8] - [10] for packet delivery, and the topology of the whole network. Other specific wireless network issues such as channel contentions and transmission errors will affect the network performance as well.. Lifetime is the key performance measure for wireless sensor network, because it is very difficult or impossible to replace the power supplies for sensor nodes after deployed. In order to prolong the network lifetime, one popular approach based on MAC-layer design is to place nodes in sleep mode periodically [2] , [3] , [6] , [7] , [17] . The sensor node works under low-power operational state [6, 11] while it is in sleep mode. The longer time the node stays in sleep mode, the more energy can be saved.. It is shown in [2, 12] that simply putting sensor nodes in sleep mode for a fixed time interval would cause the network to synchronize and may lead to deadlock. Therefore, randomizing the sleep interval was proposed in [12] - [14] to resolve the deadlock problem while conserving energy at the same time. However, the energy conservation is realized at the expenses of reduced network capacity, increased latency and deferred system response. Analytical results on the capacity of large static ad hoc network with identical nodes are presented in [14] . Few analytical models have been developed to explore the trade-off between sleep scheme (energy consumption) and network performance. In [15, 16] , the Markovian model and fluid model are developed, respectively, to analyze the homogeneous static sensor networks with random sleep scheme.. In this paper, we analyze a random sleep scheme with the assumptions that sensor nodes are randomly entering the sleep mode, and each node can be independently characterized by two exponentially distributed operational periods: Active and Sleep. In active mode, the node is fully working and able to transmit/receive packets. While in sleep mode, the node will turn off its transceiver, but continuously keep sensing the surrounding environment.. Under the preceding assumptions, an analytical model is developed to explore the impact of system parameters, such as the node sleep/active dynamics, maximum avail- able routes and the time scale of sleep-active cycle, on network performance. Specifically, we develop a queueing model for the sensor nodes, and name it as the single server queue with server shutting down in a varying neighborhood to derive the probability measures of sensor node in different operational states, such as the packet number distribution, node throughput and responsive property. Next, we develop a power consumption model, which takes the node sleep to active transition frequency into consideration, and acquire the network capacity and mean packet delay.. Our results demonstrate that the sleep/active dynamics produces the predominant impact on average power consumption and mean packet delay. Properly choosing the time scale of sleep-active cycle is vital to the design of a power-efficient sensor network. Furthermore, our analysis also yields the estimate of maximum available routes that can be used to determine the proper routing table size.. The remainder of this paper is organized as follows: Section 2 introduces the operations of wireless sensor network, and the assumptions we made to carry out our analytical framework. Section 3 develops the sensor node queueing model and gets the packet number distribution in the sensor node. In Section 4, we derive the node throughput, mean packet number and analyze the node responsive property in sleep and active states. Section 5 presents network performance measures of interest. Section 6 explores the trade-off between random sleep scheme and network performance, and develops several guidelines to design power-efficient sensor network. Finally, the conclusion and direction of future work are summarized in Section 7. This paper analyzes the wireless sensor network whereby the nodes enter sleep mode randomly, independent of each other, and transmit their data to sink node via multi-hop communication.. We derived the node queueing model to analyze the random sleep scheme, and developed an analytical framework to model the network performance. For single sensor node, we derived its node throughput, mean packet number and analyzed its responsive property. For the whole network, we derived the power consumption, capacity and mean packet delay. We explored the trade-off among the above-mentioned performance measures and validated our analytical results through extensive simulations.. We conclude that node sleep/active dynamics is the key parameter which has greatest impact on the average power consumption and mean packet delivery delay. Properly choosing the time scale of sleep-active cycle is vital to design a power-efficient sensor network.. In our current research, we have assumed an idealized MAC protocol, so one of our future works is to extend the framework to incorporate with more realistic protocol with collisions and transmission errors. In a practical sensor network, the node buffer size is finite. Evaluating the impact of buffer size on the network performance is another objective of our future work. Finally, notice that the sensor nodes may be mobile and heterogeneous, how to integrate the node mobility and heterogeneity into an analytical framework is a challenging issue. We have defined Λ k E as the equivalent packet generating rate at node k from sensing the surrounding environment and. In Section 3.1 we have formulated the sensor node behavior as a single server queue and mentioned that the internal packet arrival rate Λ k I = λ i,k a at node k will be calculated through the following network model. Now Λ k I can be obtained by solving the following network flow balance equation. where. respectively. And F is the matrix of transition probabilities between the queues in the open queueing network. Element F (k, j) represents the fraction of outgoing traffic of node k that is forwarded to its next-hop j. We present two examples ( Fig.13 and Fig.14) to illustrate the above flow balance equation. In order to obtain F, we should account for the routing policy adopted by the senor nodes as well as the joint active/sleep dynamics of all their next-hop nodes. As described in Section 3.2.1, the reference node always forwards its packets along the highest priority route associated with the lowest energy cost among all the available next-hops. Since we have assumed that the active/sleep dynamics of the next-hops are independent, we can build F by the following formula. where N k,j is the set of next-hop nodes that have higher priority than node j in the routing table of node k; and θ is a normalization factor such that the sum of F (k, j) over all j's is equal to one. The formula of F (k, j) means the probability that only node j is Active (which means node j can receive packets) and all the other next-hops with higher priority than node j are in Sleep mode. Summing up the four equations in (45), we have λ a P a + λ s P s = µP af .. (46) means in steady state, the equivalent packet arrival rate is equal to the equivalent packet service rate. The four equations in (45) are not independent, we need another equation to resolve the M

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A modal logic internalizing normal proofs In the proof-theoretic study of logic, the notion of normal proof has been understood and investigated as a metalogical property. Usually we formulate a system of logic, identify a class of proofs as normal proofs, and show that every proof in the system reduces to a corresponding normal proof. This paper develops a system of modal logic that is capable of expressing the notion of normal proof within the system itself, thereby making normal proofs an inherent property of the logic. Using a modality to express the existence of a normal proof, the system provides a means for both recognizing and manipulating its own normal proofs. We develop the system as a sequent calculus with the implication connective ⊃ and the modality , and prove the cut elimination theorem. From the sequent calculus, we derive two equivalent natural deduction systems. In the proof-theoretic study of logic, the notion of normal proof has played a central role. Conceptually a normal proof is a proof that contains no indirect reasoning and provides direct evidence of the truth it asserts. In a formal system of logic, a normal proof is a proof that contains no "detour" which introduces a connective or modality (e.g., implication ⊃, conjunction ∧, and necessity ) only to immediately eliminate it. In this sense, a normal proof is minimal in size because it does not reduce to another proof (irrespective of the size of its representation).. Traditionally the notion of normal proof has been understood and investigated as a metalogical property. Usually we formulate a system of logic, identify a class of proofs as normal proofs, and show that every proof in the system reduces to a corresponding (unique) normal proof. The result is then exploited in examining other metalogical properties of the system such as unprovability of inconsistency (⊥) and solving practical problems such as building a theorem prover. Thus, although not recognized by the system itself, normal proofs serve as an indispensable tool for succinctly characterizing the system and developing practical applications.. This paper develops a system of logic that is capable of expressing the notion of normal proof within the system itself. That is, the system has a means for internalizing and reasoning about its own normal proofs, thereby making normal proofs an inherent property of the logic (as opposed to a metalogical property). Thus the system is reflective [1] in that it is self-aware of its own normal proofs. To the best of our knowledge, no such system has been proposed.. We formulate the logic in the judgmental style of Martin-Löf [2, 3] which distinguishes between judgments and propositions. A judgment represents an object of knowledge and a proof of it allows us to know the object of knowledge. If we do not have a proof, the judgment is not part of our knowledge. In contrast, a proposition conveys no knowledge in itself, but if A is known to be a proposition, we know what counts as a verification of its truth. That is, we can check whether a proof of the truth of A is indeed valid or not. Thus the notion of judgment is independent of (and precedes in priority) the notion of proposition.. In order to deal with both ordinary proofs and normal proofs within the same system of logic, we use two separate judgments A true and A ↑ where A is a proposition, or simply a formula. A true is a truth judgment whose proof is an ordinary proof and may reduce to another proof. A ↑, adopted from the intercalation calculus of Byrnes [4] , is a normality judgment whose proof is a normal proof and does not reduce to another proof. As A ↑ states a different "mode" of truth, namely truth with a normal proof, we develop the system as "modal" logic [5] by defining a new modality to capture the metalogical property of A true expressed in A ↑. As shown by Pfenning and Davies [3] , the judgmental style lends itself particularly well to the development of systems of modal logic. In our case, we use to internalize a normality judgment within a truth judgment 1 :. A ↑ We present a system of modal logic that extends a fragment of propositional logic with the implication connective ⊃ and uses a novel modality to express the notion of normal proof within the system itself. A sequent calculus is developed to ensure that the system is sound, and then equivalent natural deduction systems are derived. The main obstacle to developing the system is to identify a form of sequent that reflects the self-referential nature of truth judgments and normality judgments. We find that only semi-normality judgments, which are a weaker form of normality judgments, can be internalized within truth judgments using .. Future work includes extending our system to full propositional logic and first-order logic, which do not require additional forms of sequents or hypothetical judgments. As the present work uses a purely proof-theoretic approach, a modeltheoretic account of the modality is another direction to pursue.. Case E =

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Precise interprocedural dataflow analysis via graph reachability The paper shows how a large class of interprocedural dataflow-analysis problems can be solved precisely in polynomial time by transforming them into a special kind of graph-reachability problem.The only restrictions are that the set of dataflow facts must be a finite set, and that the dataflow functions must distribute over the confluence operator (either union or intersection). This paper shows how to find precise solutions to a large class of interprocedural dataflow-analysis problems in polynomial time. In contrast with intraprocedural dataflow analysis, where "precise" means "meet-over-all-paths' '[ 20] , a precise inter-procedural dataflow-analysis algorithm must provide the "meet-over-all-valid-paths" solution.. (A path is valid if it respects the fact that when a procedure finishes it returns to the site of the most recent call [31, 15, 6, 24, 21, 29 ]-see Section 2.) Relevant previous work on precise interprocedural dataflow analysis can be categorized as follows: q Polynomial-time algorithms for specific individual problems (e.g., constant propagation [5, 14] , flowsensitive summary information [6] , and pointer analysis [241) . o A polynomial-time algorithm for a limited class of problems: the locally separable problems (the interprocedural versions of the classical "bit-vector" or "gen+Work performed while visiting the Datatogisk Institut, University of Permission to copy wfthout fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advanta~e, the ACM copyright notice and the title of the publication and Its date appear, and notice is given that copying is by permission of the Association of Computing Machinery. To ecrpyotherwise, or to republish, requires a fee and/or specific permission. POPL '951/95 San Francisco CA USA 0 1995 ACM O-89791-892-l/9WOOOl ....$3.50 kill" problems), which include reaching definitions, available expressions, and live variables [22] . . Algorithms for a very general class of problems [10, 31, 21] .. The work cited in the third category concentrated on generality and did not provide polynomial-time algorithms. In contrast to this previous work, the present paper provides a polynomial-time algorithm for finding precise solutions to a general class of interprocedural dataflow-analysis problems. This class consists of all problems in which the set of dataflow facts D is a finite set and the dataflow functions (which are in 2~+ 2~) distribute over the meet operator (either union or intersection, depending on the problem).. We will call this class the interprocedurai, finite, distributive, subset problems, or IFDS problems, for short, All of the locally separable problems are IFDS problems. In addition, many non-separable problems of practical importance are also IFDS problems-for example: truly-live variables [13] , copy constant propagation [12, pp. 660] , and possibly-uninitialized variables. Our results are based on two insights: (i) By restricting domains to be powersets of atomic dataflow facts and dataflow functions to be distributive, we are able to efficiently create simple representations of functions that summarize the effects of procedures (by supporting efficient lookup operations from input facts to output facts). For the locally separable problems, the representations of summary functions are sparse. This permits our algorithm to be as efficient as the most efficient previous algorithm for such problems, but without losing generality.. (ii) Instead of calculating the worst-case cost of our algorithm by determining the cost-per-iteration of the main loop and multiplying by the number of iterations, it is possible to break the cost of the algorithm down into three contributing aspects and bound the total cost of the operations performed for each aspect (see the Appendix).. The most important aspects of our work can be summarized as follows:. In Section 3, we show that all IFDS problems can be solved precisely by transforming them into a special kind of graph-reachability problem: reachability along interprocedurally realizable paths. In contrast with ordinary reachability problems in directed graphs (e.g., transitive closure), realizable-path reachability problems involve some constraints on which paths are considered. A realizable path mimics the call-return structure of a program's execution, and only paths in which "returns" can be matched with corresponding "calls" are considered. In Section 4, we present a new polynomial-time algorithm for the realizable-path reachability problem. The algorithm runs in time O (ED 3); this is asymptotically Jaster than the best previously known algorithm for the problem [16] , which runs in time * q © q O (D3~CallPEP +-D4~Cal$).. As cii~cussed in Sect~on 5, the new realizable-path reachability algorithm is adaptive, with asymptotically better performance when applied to common kinds of problem instances that have restricted form. For example, there is an asymptotic improvement in the algorithm's performance for the common case of locally separable problems. Our work generalizes that of Knoop and Steffen [22] in the sense that our algorithm handles a much larger class of problems, yet on the locally separable problems the algorithm runs in the same time as that used by the Knoop-Steffen algorithm-O (ED). Imprecise (overly conservative) answers to interprocedural dataflow-analysis problems could be obtained by treating each interprocedural dataflow-analysis problem as if it were essentially one large intraprocedural problem.. In graph-reachability terminology, this amounts to considering all paths rather than considering only the interprocedurally realizable paths. For the IFDS problems, we can bound the extra cost needed to obtain the more precise (realizable-path) answers. In the important special case of locally separable problems, there is no "penalty" at all-both kinds of solutions can be obtained in time O (ED). In the distributive case, the penalty is a factor of D: the running time of our realizable-path reachability algorithm is O (ED 3), whereas all-paths reachability solutions can be found in time O (ED 2). However, in the preliminary experiments reported in Section 6, which involve examples where D is in the range 70-142, the penalty observed is at most a factor of 3.4. Callahan has given algorithms for several "interprocedural flow-sensitive side-effect problems" [6] . Although these problems are (from a certain technical standpoint) of a slightly different character from the IFDS dataflow-analysis problems, with small adaptations the algorithm from Section 4 can be applied to these problems and is asymptotically faster than the algorithm given by Callahan. In addition, our algorithm handles a natural generalization of Callahan's problems (which are locally separable problems) to a class of distributive flow-sensitive side-effect problems. (This and other related work is described in Section 7.) The realizable-path reachability problem is also the heart of the problem of interprocedural program slicing, and the fastest previously known algorithm for the problem is the one given by Horwitz, Reps, and Binkley [16] The IFDS framework is designed to be as general as possible (in particular, to support languages with procedure calls, parameters, and both global and local variables). Any problem that can be specified in this framework can be solved efficiently using our algorithms; semantic correctness is an orthogonal issue. A problem designer who wishes to take advantage of our results has two obligations: (i) to encode the problem so that it meets the conditions of our framework; (ii) to show that the encoding is consistent with the programming language's semantics [9, 10] . Encoding a problem in the IFDS framework may involve some loss of precision. For example, in languages in which parameters are passed by reference there may be a loss of precision for problem instances in which there is aliasing. However, the process of finding the solution to the resulting IFDS problem introduces no further loss of precision.. To specify the IFDS framework, we need the following definitions:. Definition 2,1. In the IFDS framework, *a p$ogram is represented using a directed graph G = (N , E ) called a supergraph.. G consists of a collection of flow graphs G~, G2, " " (one for each procedure), one of which, Groin, represents the program's main procedure. Each flowgraph G has a unique start node SP, and a unique exit node eP. T~e other nodes of the flowgraph represent the statements and predicates of the procedure in the usual way, except that a procedure call is represented by two nodes, a call node and a return-site node. (The sets of call and returnsite nodes of procedure p will be denoted by CallP and Ret , respectively; the sets of all call and return-site nodes L in t e supergraph will be denoted by Call and Ret, respectively.) In addition to the ordinary intraprocedural edges that connect the nodes of the individual flowgraphs, for each procedure* call, represented by call-node c and return-site node r, G has three edges: o An intraprocedural call-to-return-site edge from c to n q An interprocedural call-to-start edge from c to the start node of the called procedure; (The call-to-return-site edges are included so that the IFDS framework can handle programs with local variables and parameters. The dataflow functions on call-to-returnsite and exit-to-return-site edges permit the information about local variables that holds at the call site to be combined with the information about global variables that holds at the end of the called procedure.). When discussing time and space requirements, we use the name of a set to denote the set's size. For example, we use Call, rather thqn I Call 1, to denote the number of call nodes in graph G . (We make two small de~iatious fr~m this convention, using N and E to stand for IN I and I E 1, respectively.) Example. Figure 1 shows an example program and its supergraph G . u Definition 2.2. A path of length j from node m to node n is a (possibly empty) sequence of j edges, which will be denoted by [el, e2, " " " , ej] , such that for all i, 1< i <j-1, the target of edge ei is the source of edge ei + 1.

B O B O O B B O B O O O O B O O O O O O O O O B O O O O O O O O O O O O O O O O O O B O O O O O O O O O B O O O O O O O O O O B O B O O O O B O O O O B O O O O O B O O O O O B O O B O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O B O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O B O O O O B O O O O O B O O O O O O O O O B O O O O O O O O B O O O O O O O O O O O O O O B O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O B O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O B O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O B O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Simple environment for developing methods of controlling chaos in spatially distributed systems The paper presents a simple mathematical model called a coupled map lattice (CML). For some range of its parameters, this model generates complex, spatiotemporal behavior which seems to be chaotic. The main purpose of the paper is to provide results of stability analysis and compare them with those obtained from numerical simulation. The indirect Lyapunov method and Lyapunov exponents are used to examine the dependence on initial conditions. The net direction phase is introduced to measure the symmetry of the system state trajectory. In addition, a real system, which can be modeled by the CML, is presented. In general, this article describes basic elements of environment, which can be used for creating and examining methods of chaos controlling in systems with spatiotemporal dynamics. Deterministic chaos is complex behavior which can be generated by a nonlinear dynamic system as a result of state trajectory evolution when its previous history is known (Ott, 2002) . The origin of this phenomenon in nonlinear dynamic systems is connected with their sensitivity to initial conditions. In fact, chaotic behavior is a common phenomenon discovered in physics (liquids (Procaccia and Meron, 1986; Langenberg et al., 2004) , lasers (Yamada and Graham, 1980; Used and Martin, 2010) , plasma (Held et al., 1984; Banerjee et al., 2010) ), mechanics (Chui and Ma, 1982; Ott, 2002) , electronics (Gunaratne et al., 1989; Yim et al., 2004) , chemistry (Argoul et al., 1987; Córdo-ba et al., 2006) , biology (action of human heart (Govindan et al., 1998) and brain (Andrzejak et al., 2001; Gautama et al., 2003) ), and in many other branches of science and industry.. Chaotic systems, due to their sensitivity to initial conditions, are unpredictable but, as has been proved, they can be effectively controlled (Ott et al., 1990; Singer et al., 1991; Dressler and Nitsche, 1992; Chen and Dong, 1993; Alsing et al., 1994; Pyragas, 2001; Andrievskii and Fradkov, 2003) . The control of chaos in such a type of system is considered a process which changes an irregular and unpredictable behavior to a well-ordered and periodical one. Sensitivity to initial conditions is particularly important in real, physical systems. For example, a chaotic behavior in chemical reactors can cause unpredictable and negative results. Moreover, many real systems and their mathematical models represent similar spatiotemporal behaviors, where chaos can be observed both in time and space. As has been shown, chaos in spatially distributed dynamical systems can also be controlled (Auerbach, 1994; Astakhov et al., 1995; Parmananda, 1997; Parekh et al., 1998; Zhu and Chen, 2001; Mihaliuk et al., 2002; Beck et al., 2002; Boukabou and Mansouri, 2005) . This makes this issue even more essential and it seems that it could have numerous practical applications (i.e., chemical reactors, lasers, plasma).. The main purpose of the paper is to provide results of both analytical and numerical research regarding CML system stability. In addition, we found it very important to chose and present proper tools which can be useful during the examination of the system sensitivity to initial conditions. Based on measurements of this property and the level of state trajectory symmetry, some conclusions about the existence of chaos in the system can be made.. The presented model and tools can be helpful while creating and checking new algorithms of controlling chaos for spatiotemporal systems. It is even more essential as its potential, physical application is presented. In general, this article describes basic elements of environment which can be used for creating and examining methods of con- As was shown in this paper, the coupled map lattice is a simple mathematical model which generates complex, chaotic spatiotemporal behaviors for some range of its parameters. Based on the indirect Lyapunov method, the analysis of system stability was performed. Analytical results were compared with those obtained from numerical simulation. To review the existence of chaos during numerical studies, Lyapunov exponents and the net direction phase were introduced. Scenarios of transition to chaos in time and space domains were also provided. In addition, a real system which can be modeled by CMLs was presented. To sum up, the article described basic elements of the environment, which can be used for modeling spatiotemporal chaos. The presented model and tools can be also helpful while creating and examining algorithms of controlling chaos.

O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O B I O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O


Adjustable Speed Surface Subdivision We introduce a non-uniform subdivision algorithm that partitions the neighborhood of an extraordinary point in the ratio σ : 1 − σ, where σ ∈ (0, 1). We call σ the speed of the non-uniform subdivision and verify C 1 continuity of the limit surface. For σ = 1/2, the Catmull-Clark limit surface is recovered. Other speeds are useful to vary the relative width of the polynomial spline rings generated from extraordinary nodes. To be able to control and adjust, possibly repeatedly, the relative width of the polynomial surface rings generated by a Catmull-Clark-like subdivision algorithm (see Figure 1 ), we derive rules for a new class of non-uniform surface subdivision algorithms. The resulting family of algorithms has properties akin to Catmull-Clark subdivision and can in particular generate the limit surface of Catmull-Clark subdivision. Figure 8 shows an application where fast filling of a n-sided surface hole is advantageous. In general, the fill speed must depend on the application since the surface quality deteriorates for more rapid fills. We have also used the characteristic rings of adjustable speed subdivision as concentric tessellation map of guided subdivision surfaces [KP07b] , where the speed controls the parameterization rather than the shape (see Figure 9 ). The theory is advanced by the paper in that it explores a non-traditional approach that allows analyzing the resulting non-uniform subdivision surface. able. Instead of subdividing uniformly, we locally subdivide in a ratio σ :σ where σ ∈ (0, 1) andσ := 1 − σ. We call σ the speed of the non-uniform subdivision. Since splines are invariant when scaling all knots uniformly or when translating the knot sequence, only the knot spacing is in the following of interest. σ σσ σ } tensored (top) for adjustable speed subdivision. (right) Consistent knot spacings around an extraordinary node of valence n = 5. The corresponding surface is a sequence of C 2 -connected surface rings of degree bi-3.. Tensoring this subdivision, as shown in Figure 3 , we obtain an adjustable speed subdivision that is well-defined except near vertices with n = 4 neighbors. Adding rules for these extraordinary cases, we obtain a family of subdivision algorithms generating a sequence of polynomial surface rings of degree bi-3 with contraction speed σ ∈ (0, 1). After reviewing the related literature, we derive the rules for adjustable speed subdivision in Section 2. In Section 3, we verify properties of adjustable speed subdivision and in Section 4, we discuss some applications.

B I O B O O O B B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O B O B O O O O O O O O O O O B O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I B O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O B I B O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I B O O O O O O O O O O B I B O O O O O O O O


Generalized Spatio-Chromatic Diffusion In this paper, a framework for diffusion of color images is presented. The method is based on the theory of thermodynamics of irreversible transformations, which provides a suitable basis for designing correlations between the different color channels. More precisely, we derive an equation for color evolution, which comprises a purely spatial diffusive term and a nonlinear term that depends on the interactions among color channels over space. We apply the proposed equation to images represented in several color spaces, such as RGB, CIELAB, Opponent colors and IHS Even though color information is essential to many vision tasks, most biological and computational vision models work exclusively in the luminance domain. As a consequence, research has been focused mainly on sources of information such as intensity gradients, textural features, or geometrical cues. However, data from biological vision systems show that boundary representations do not segregate achromatic and chromatic signals into different representations but, rather, they pool signals from all chromatic and achromatic sources in order to generate the most accurate boundaries possible in response to any given stimulus array [1] . Interestingly, a firm theoretical basis for such a claim has been provided by computer vision [2] . Namely, it has been shown that the effectiveness of different edge operators, as theoretically measured by Chernoff information, can improve by using either multiscale processing and chromaticity in addition to greyscale. However, these results leave open the very issue of how to combine, in a single representation, multiscale processing and color. In computer vision, multiscale representations of a grey level image I have been obtained by fine-to-coarse transformations that can be modelled, in general, by a diffusion or heat equation [3] , [4] ,. where D is the diffusivity or conductance, a constant which, without loss of generality, is usually set equal to 1, ∂ t denotes the partial derivative ∂/∂t and ∇ 2 is the Laplacian operator. A vast amount of research on diffusion processes can be found in the computer and computational vision literature mostly devoted to monochromatic images (for an in depth treatment, see [5] , [6] , [7] ).. A vector-valued (multi-valued) image is a smooth mapping from the image domain Ω ⊆ R 2 to an m-dimensional range, I : Ω → R m ; in other terms, it is a set of single-valued images, or channels, sharing the same domain, i.e., I(r) = (I i (r)) T , where i = 1, ..., m and r= (x, y) denotes a point in Ω. A color image can be considered a vector-valued image of three components (m = 3) or color channels.. A number of authors [8] , [9] , [10] , [11] have addressed vector-valued diffusion by extending to R m scalar anisotropic diffusion schemes ( [6] , [12] ). For instance, Whitaker and Gerig [8] obtain vector-valued anisotropic diffusion through a system of singlevalued diffusion processes, evolving simultaneously but sharing a common conductance modulating term d, namely ∂ t I i = ∇·(d(kJ k)∇I i ), where kJ k is the Euclidean norm of the generalized Jacobian matrix of I (for notational convenience, we simply write I i (r) as I i ). Analogously, Weickert [9] proposes a common conductance d which takes into account information from all channels as a function of the structure tensor for vector images, M ρ (∇I σ ) = P m i=1 M ρ (∇I i,σ ), where M ρ (∇I i,σ ) = K ρ * (∇I i,σ ∇I T i,σ ). is the scalar structure tensor or second-moment matrix, K ρ being a Gaussian kernel, ρ and σ the integration and noise scales, respectively (ρ À σ). The function d is designed to allow maximal smoothing along a coherence direction determined via the eigenvector corresponding to the smallest eigenvalue of the structure tensor. A different approach has been proposed in [10] by considering color images as surfaces.. In this case transitions from fine to coarse scale of resolution can be generated by a suitable choice of the metric tensor. In particular the so-called Beltrami flow is governed by the equation. x 2 = y, g µν is the metric tensor and g is its determinant. In a similar vein, Sapiro and Ringach [11] choose d as a decreasing function of (λ + − λ − ),where λ + and λ − are the eigenvalues of the metric tensor, and diffusion is constrained to occur normal to the direction of maximal change. Interestingly, all such anisotropic models relax, in the isotropic limit, to a system of single-valued, scalar partial differential equations (PDEs), each taking place on a separate channel I i , with ∂ t I i = ∇ 2 I i (Independent Channel Diffusion, ICD). For instance, the Laplace-Beltrami operator reduces to the ordinary Laplacian when g is the Euclidean metric.. Here a different perspective to the problem is presented, founded on the concept of color channel interactions in the framework of the thermodynamics of open systems. It will be shown that, by considering the different channels as interact-4 ing systems, a generalized diffusion equation can be derived that determines the evolution in spatio-chromatic scale space, (Generalized Spatio-chromatic Diffusion, GSCD), without being constrained by a particular form of diffusivity. As a result, the evolution equation across scales comprises a purely diffusive term and a nonlinear term that depends on the interactions between channels. In this respect, our approach shares some common aspects either with other approaches, that derive systems of diffusion equations in a variational framework, for instance [13] , [14] , the latter being specifically conceived for chromaticity diffusion, or with pseudo-linear scale-spaces recently introduced by Florack [15] . The proposed diffusion scheme is intended mainly to provide a preprocessing step to later specialized stages of visual analysis; meanwhile, as it will be shown in the sequel, it exhibits appreciable noise suppression properties. Also, a possible anisotropic extension of GSCD will be discussed. A variety of color spaces can be used to deal with color images, there is a variety of spaces and no theoretical method has been developed to choose the most appropriate with respect to a problem at hand; the number of variables involved in practical applications makes such choice unfeasible. For this reason we have not restricted our analysis to a specific space, but rather, we have carried out experiments in a variety of spaces.

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