Stochastic Unsplittable Flows

We consider the stochastic unsplittable flow problem: given a graph with edge-capacities, and source-sink pairs with each pair having a size and a value, the goal is to route the pairs unsplittably while respecting edge capacities to maximize the total value of the routed pairs. However, the size of each pair is a random variable and is revealed only after we decide to route that pair. Which pairs should we route, along which paths, and in what order so as to maximize the expected value? We present results for several cases of the problem under the no-bottleneck assumption. We show a logarithmic approximation algorithm for the single-sink problem on general graphs, considerably improving on the prior results of Chawla and Roughgarden which worked for planar graphs. We present an approximation to the stochastic unsplittable flow problem on directed acyclic graphs, within less than a logarithmic factor of the best known approximation in the non-stochastic setting. We present a non-adaptive strategy on trees that is within a constant factor of the best adaptive strategy, asymptotically matching the best results for the non-stochastic unsplittable flow problem on trees. Finally, we give results for the stochastic unsplittable flow problem on general graphs. Our techniques include using edge-confluent flows for the single-sink problem in order to control the interaction between flow-paths, and a reduction from general scheduling policies to "safe" ones (i.e., those guaranteeing no capacity violations), which may be of broader interest

Central nervous system manifestations in HIV: magnetic resonance imaging pictorial review

Human immunodeficiency virus (HIV) is a member of the Retroviridae (retrovirus) family. It is associated with immunodeficiency, neurological diseases and neoplasms. With the use of antiretroviral therapy (ART), the prognosis of people who are infected with HIV has improved, and the incidence of HIV-related central nervous system (CNS) diseases has markedly decreased. In spite of that the mortality from HIV-related CNS diseases remains significant. Magnetic resonance imaging (MRI) has improved the perspective for people with HIV with the help of early diagnosis and prompt treatment. There are various conditions which come under the spectrum of CNS manifestations of HIV for e.g., HIV encephalopathy, progressive multifocal leukoencephalopathy (PML), HIV-related primary CNS lymphoma (PCNSL), CNS toxoplasmosis, other diseases caused by opportunistic infections like CNS cryptococcosis, CNS tuberculosis and immune reconstitution inflammatory syndrome (IRIS). Each condition shows certain specific MRI features which aid in diagnosis. Although, distinguishing between HIV-related CNS diseases based on imaging alone is sometimes difficult, in this review, we discuss the spectrum and imaging features that can contribute to their early differentiation

A Low-Cost Lane-Following Algorithm for Cyber-Physical Robots

Duckiebots are low-cost mobile robots that are widely used in the fields of research and education. Although there are existing self-driving algorithms for the Duckietown platform, they are either too complex or perform too poorly to navigate a multi-lane track. Moreover, it is essential to give memory and computational resources to a Duckiebot so it can perform additional tasks such as out-of-distribution input detection. In order to satisfy these constraints, we built a low-cost autonomous driving algorithm capable of driving on a two-lane track. The algorithm uses traditional computer vision techniques to identify the central lane on the track and obtain the relevant steering angle. The steering is then controlled by a PID controller that smoothens the movement of the Duckiebot. The performance of the algorithm was compared to that of the NeurIPS 2018 AI Driving Olympics (AIDO) finalists, and it outperformed all but one finalists. The two main contributions of our algorithm are its low computational requirements and very quick set-up, with ongoing efforts to make it more reliable

Customer Perceived Value- Challenges and Opportunities of Indian Retail Stores

Over the period of time, the significance of shopping has transformed for the customers. It was just a requirement for them initially. Shopping and retailing was used to be a very easy concept in India, buying the products required from the traditional local stores from the nearest place. The change has brought up by the western companies. The factors that influenced the store choice have also changed. The customers are not just looking for the products, but also attracts from space, convenience and ambience and furthermore large variety of products under one roof. Shopping is not merely a necessity now. These factors are beginning to play avital role in magnetizingthe potential customers. Many huge international companies like Wal-Mart have penetrated the Indian market and are trying to steal the customers from the traditional unorganized market. There is definitely a lot of growth in the organized sector and the unorganized sector needs to cope up with the latest trends of the market. This assignment’s purpose is to study the changing customer perception and craze of modern Indian retail market. The customers are now moving from the traditional retail stores to the new and improvised organized retail shops. In order to perform this research, semi structured interviews from the Indian customers have played the main role as a tool. Several elements on which the customers center their choice of retail stores are analyzed in this research regarding the organized as well as the unorganized retailers

Automatic generation of social network posts for private domains

This disclosure describes techniques to generate a stream of content related to the interests of users in a social media platform. The social media platform is private, e.g., restricted to a private domain, e.g., within a company or organization. The content includes social networking posts that are automatically generated from public sources, such as web URLs. A bot is deployed to scan web URLs periodically to identify recent content that is relevant and likely of interest to users within the domain. A social media post, e.g., including an automatically generated summary and/or an image is generated. Users within the private domain can communicate and share commentary on the social media post. This enables users within a domain to discover content of interest and to have a secure forum for discussion

The Even-Path Problem in Directed Single-Crossing-Minor-Free Graphs

Finding a simple path of even length between two designated vertices in a directed graph is a fundamental NP-complete problem [Andrea S. LaPaugh and Christos H. Papadimitriou, 1984] known as the EP problem. Nedev [Zhivko Prodanov Nedev, 1999] proved in 1999, that for directed planar graphs, the problem can be solved in polynomial time. More than two decades since then, we make the first progress in extending the tractable classes of graphs for this problem. We give a polynomial time algorithm to solve the EP problem for classes of H-minor-free directed graphs, where H is a single-crossing graph. We make two new technical contributions along the way, that might be of independent interest. The first, and perhaps our main, contribution is the construction of small, planar, parity-mimicking networks. These are graphs that mimic parities of all possible paths between a designated set of terminals of the original graph. Finding vertex disjoint paths between given source-destination pairs of vertices is another fundamental problem, known to be NP-complete in directed graphs [Steven Fortune et al., 1980], though known to be tractable in planar directed graphs [Alexander Schrijver, 1994]. We encounter a natural variant of this problem, that of finding disjoint paths between given pairs of vertices, but with constraints on parity of the total length of paths. The other significant contribution of our paper is to give a polynomial time algorithm for the 3-disjoint paths with total parity problem, in directed planar graphs with some restrictions (and also in directed graphs of bounded treewidth)

Mosaic Variant of Turner Syndrome

Turner syndrome is the most common chromosomal abnormality leading to gonadal failure and primary amenorrhea. While half of the cases have monosomy of chromosome X, the remaining exhibit mosaicism resulting in wide variation of phenotypic characteristics and clinical manifestations. We present a case of a 24-year-old female with mosaic variant Turner syndrome. The diagnosis was confirmed by karyotype analysis and laparoscopy

The Even-Path Problem in Directed Single-Crossing-Minor-Free Graphs

Finding a simple path of even length between two designated vertices in a directed graph is a fundamental NP-complete problem known as the EvenPath problem. Nedev proved in 1999, that for directed planar graphs, the problem can be solved in polynomial time. More than two decades since then, we make the first progress in extending the tractable classes of graphs for this problem. We give a polynomial time algorithm to solve the EvenPath problem for classes of H-minor-free directed graphs,1 where H is a single-crossing graph. We make two new technical contributions along the way, that might be of independent interest. The first, and perhaps our main, contribution is the construction of small, planar, parity-mimicking networks. These are graphs that mimic parities of all possible paths between a designated set of terminals of the original graph. Finding vertex disjoint paths between given source-destination pairs of vertices is another fundamental problem, known to be NP-complete in directed graphs, though known to be tractable in planar directed graphs. We encounter a natural variant of this problem, that of finding disjoint paths between given pairs of vertices, but with constraints on parity of the total length of paths. The other significant contribution of our paper is to give a polynomial time algorithm for the 3-disjoint paths with total parity problem, in directed planar graphs with some restrictions (and also in directed graphs of bounded treewidth)