Bifurcations of piecewise smooth flows:perspectives, methodologies and open problems

In this paper, the theory of bifurcations in piecewise smooth flows is critically surveyed. The focus is on results that hold in arbitrarily (but finitely) many dimensions, highlighting significant areas where a detailed understanding is presently lacking. The clearest results to date concern equilibria undergoing bifurcations at switching boundaries, and limit cycles undergoing grazing and sliding bifurcations. After discussing fundamental concepts, such as topological equivalence of two piecewise smooth systems, discontinuity-induced bifurcations are defined for equilibria and limit cycles. Conditions for equilibria to exist in n-dimensions are given, followed by the conditions under which they generically undergo codimension-one bifurcations. The extent of knowledge of their unfoldings is also summarized. Codimension-one bifurcations of limit cycles and boundary-intersection crossing are described together with techniques for their classification. Codimension-two bifurcations are discussed with suggestions for further study

Optimizing egalitarian performance in the side-effects model of colocation for data center resource management

In data centers, up to dozens of tasks are colocated on a single physical machine. Machines are used more efficiently, but tasks' performance deteriorates, as colocated tasks compete for shared resources. As tasks are heterogeneous, the resulting performance dependencies are complex. In our previous work [18] we proposed a new combinatorial optimization model that uses two parameters of a task - its size and its type - to characterize how a task influences the performance of other tasks allocated to the same machine. In this paper, we study the egalitarian optimization goal: maximizing the worst-off performance. This problem generalizes the classic makespan minimization on multiple processors (P||Cmax). We prove that polynomially-solvable variants of multiprocessor scheduling are NP-hard and hard to approximate when the number of types is not constant. For a constant number of types, we propose a PTAS, a fast approximation algorithm, and a series of heuristics. We simulate the algorithms on instances derived from a trace of one of Google clusters. Algorithms aware of jobs' types lead to better performance compared with algorithms solving P||Cmax. The notion of type enables us to model degeneration of performance caused by using standard combinatorial optimization methods. Types add a layer of additional complexity. However, our results - approximation algorithms and good average-case performance - show that types can be handled efficiently.Comment: Author's version of a paper published in Euro-Par 2017 Proceedings, extends the published paper with addtional results and proof

Triality in Minimal Model Holography

The non-linear W_{\infty}[\mu] symmetry algebra underlies the duality between the W_N minimal model CFTs and the hs[\mu] higher spin theory on AdS_3. It is shown how the structure of this symmetry algebra at the quantum level, i.e. for finite central charge, can be determined completely. The resulting algebra exhibits an exact equivalence (a`triality') between three (generically) distinct values of the parameter \mu. This explains, among other things, the agreement of symmetries between the W_N minimal models and the bulk higher spin theory. We also study the consequences of this triality for some of the simplest W_{\infty}[\mu] representations, thereby clarifying the analytic continuation between the`light states' of the minimal models and conical defect solutions in the bulk. These considerations also lead us to propose that one of the two scalar fields in the bulk actually has a non-perturbative origin.Comment: 29 pages; v2. Typos correcte

Planar Embeddings with Small and Uniform Faces

Motivated by finding planar embeddings that lead to drawings with favorable aesthetics, we study the problems MINMAXFACE and UNIFORMFACES of embedding a given biconnected multi-graph such that the largest face is as small as possible and such that all faces have the same size, respectively. We prove a complexity dichotomy for MINMAXFACE and show that deciding whether the maximum is at most $k$ is polynomial-time solvable for $k \leq 4$ and NP-complete for $k \geq 5$. Further, we give a 6-approximation for minimizing the maximum face in a planar embedding. For UNIFORMFACES, we show that the problem is NP-complete for odd $k \geq 7$ and even $k \geq 10$. Moreover, we characterize the biconnected planar multi-graphs admitting 3- and 4-uniform embeddings (in a $k$-uniform embedding all faces have size $k$) and give an efficient algorithm for testing the existence of a 6-uniform embedding.Comment: 23 pages, 5 figures, extended version of 'Planar Embeddings with Small and Uniform Faces' (The 25th International Symposium on Algorithms and Computation, 2014

An Advanced Pavement Management System based on a Genetic Algorithm for a Motorway Network

Maintenance and improvement, through the rehabilitation, of the road infrastructure is a strategic and priority objective for road agencies, nevertheless the economic resources required are often inadequate. Within road management, the pavement management system (PMS) plays an essential role because of both the money needed and the performance that should be provided in terms of safety, ride quality and transport cost. The PMS is based on searching for a balanced solution between the lowest cost and the increased level of performance (i.e. pavement condition). In this paper a PMS multi-objective optimization method, was proposed, using a genetic algorithm (GA) to identify the best solution considering different rehabilitation strategies. The multi-objective optimization GA permits a set of optimal solutions (the Pareto solution set) that takes into account all the considered constraints. Finally on the basis of a specific criteria the best solution was selected in relation to the ranking of the priorities of the agency. A detailed numerical study was conducted on the Italian A18 motorway and the results showed that the proposed model PMS-GA is a suitable support to the decision making process

An autosomal trisomy in cattle

International audienc

Contralateral prophylactic mastectomies. Correlations between primary tumor and histological findings of controlateral breast

Backgound: In Italy in 2015 48,000 new cases of breast carcinomas were diagnosed. Women who are diagnosed with breast cancer have a significant risk of developing contralateral breast cancer during the rest of their lives and this risk is closely associated to the family history, to the onset of breast cancer at a young age and is expressed at about 0.5 to 1% of metachronous tumors per year. The purpose of this work was to evaluate which and how many neoplastic lesions were seen in the contralateral breast that underwent prophylactic mastectomy and to understand what factors predict the appearance of such lesions. Methods: 168 bilateral mastectomies were analyzed in patients with an average age of 47 years, carried out from July 2008 to April 2016, at the Breast Unit of the Sant’Andrea Hospital. We considered women of any age suffering from unilateral breast cancer without either clinical or radiological evidence of a malignant lesion in the contralateral breast and negative for mutations of the BRCA1-BRCA2 genes test. Of the 168 bilateral mastectomies 35 patients were excluded from the study because they underwent neoadjuvant chemotherapy, another 35 patients because they were suffering from a bilateral neoplasia and 7 cases because they had mutated BRCA1 or BRCA2 genes. Therefore the remaining 91 patients were included in the study. Results: Both the histological features of the primary tumor and any lesions found in the contralateral prophylactic breast were analyzed. Histological examination of the main breast showed 59 cases of Invasive Ductal Carcinoma (IDC), 17 cases of Invasive Lobular Carcinoma (ILC), 9 cases of In Situ Ductal Carcinoma (ISDC), 3 microinvasive ductal, 1 invasive tubular carcinoma, 1 in situ lobular and 1 widespread in situ. In the contralateral breast, the definitive histological examination revealed that 47 patients had an occult lesion in the prophylactic contralateral breast; in particular 2 cases of LIN 1, 7 cases of LIN2, 6 cases of lobular carcinoma in situ, 26 between DIN1A/DIN1A-B/DIN1B, 4 cases of carcinoma in situ and 2 cases of Invasive Ductal Carcinoma. The correlation obtained from the observation of the main tumor has shown that in a total of 59 invasive ductal carcinoma 32 have a controlateral occult lesions and in a total of 17 cases of invasive lobular carcinoma 9 have an occult lesion in the prophylactic breast. Of these lesions, the multicentric relationship is that 50% of invasive ductal and invasive lobular carcinoma of the main breast have a contralateral lesion. Conclusion: In conclusion we would like to remind, as demonstrated by our follow-up data and as the literature reiterates, that this surgery does not improve patient survival. Certainly patients with unilateral breast cancer have many surgical therapies to be able to deal with not only having a bilateral mastectomy. The end point of this work is try to understand the risk factors of having a contralateral breast lesion to reduce the probability of a metachronous cance

Co-located Photo-Sharing on Mobile Devices

Recent years have seen great advances in the field of mobile device technology and digital photography. These advances have resulted in a significant increase in popularity of such devices. Despite this rise in popularity, technology aimed at facilitating the sharing of the digital photographs using mobile devices is still limited. This paper aims to further the research into such technology, by detailing the creation of an application, for use in co-located sharing of digital photographs, on mobile devices. The application, nicknamed FunkyShare, will allow users to share photographs in a group setting. Our application proposes to take advantage of the digital photographs format and mobile devices technology, to enhance the sharing experience and promote photo-based storytelling. A user centred design process is used in the iterative development and evaluation of two software prototypes. Prototype evaluations, in the form of user experiments, yielded several results, from which new requirements for future prototype iterations are elicited. These requirements form a concrete basis for any future work on an application of this nature

Sensory perception in preschool children affected by autism spectrum disorder: A pilot study

Introduction: Autism spectrum disorder (ASD) is a behavioral syndrome caused by a developmental disorder, biologically determined, with onset in the first three years of life. The areas concerned are mainly those related to social communication, social interaction and mutual functional and symbolic play. In the last decades, different conceptions of autism have taken, also emphasizing different sensory-perceptual abnormalities as the basis of the central features of disorder. This pilot study intends to address the issue of sensory perception in preschool children affected by ASD. Material and methods: 11 ASD children were enrolled (7 males, 4 female) aged between 2.3 years and 4.6 years, (mean age 3.29 \ub1 0.72). The control group consisted of 24 typical developing children (15 males, 9 females) (mean age 3.08 \ub1 0.87). All subjects underwent assessment of sensory perceptual abilities according to the Bogdashina's Sensory Profile Checklist Revised (SPCR) evaluation (43). Results: The two groups are comparable for age (p = 0.491) and sex distribution (p = 0.755). Table 1 shows the comparison between the two groups results in the SPCR, specifically, individuals with ASD, showed significantly higher scores on near all perception areas evaluated than healthy controls, suggesting a clear perceptual impairment in ASD subjects. Only for olfactory perception two groups were comparable. Conclusions: no significant differences in behavioral reaction to smell stimulation between ASD and typical developing children, and this result could be explained according to the early age of our sample that could cause high reactivity to smell stimulation also in typical developing examined children

Supersymmetric holography on AdS3

The proposed duality between Vasiliev's supersymmetric higher spin theory on AdS3 and the 't Hooft limit of the 2d superconformal Kazama-Suzuki models is analysed in detail. In particular, we show that the partition functions of the two theories agree in the large N limit.Comment: 25 pages, 3 figures, improved fig.