The Jamio{\l}kowski isomorphism and a conceptionally simple proof for the correspondence between vectors having Schmidt number kk and kk-positive maps

Positive maps which are not completely positive are used in quantum information theory as witnesses for convex sets of states, in particular as entanglement witnesses and more generally as witnesses for states having Schmidt number not greater than k. It is known that such witnesses are related to k-positive maps. In this article we propose a new proof for the correspondence between vectors having Schmidt number k and k-positive maps using Jamiolkowski's criterion for positivity of linear maps; to this aim, we also investigate the precise notion of the term "Jamiolkowski isomorphism". As consequences of our proof we get the Jamiolkowski criterion for complete positivity, and we find a special case of a result by Choi, namely that k-positivity implies complete positivity, if k is the dimension of the smaller one of the Hilbert spaces on which the operators act.Comment: 9 page

Energy Consumption, Trade and GDP: A Case Study of South Asian Countries

Acute shortage of energy sources in developing countries in general and South Asian countries in particular has shown that energy has become a binding input for any production process. Nowadays operation of heavy machinery and electrical equipment, and transportation of raw material and final products from their place of origination to their destination require heavy consumption of energy in one form or the other. Therefore, energy consumption that was previously ignored in the production function of a firm and an economy is now considered a vital input in production process. It affects GDP directly as by increasing energy consumption; more output can be produced with given stock of capital and labor force in a country. Also uninterrupted availability of energy at reasonable cost improves competiveness of home products in international markets and thus increases exports of home country a great deal. Resulting increase in net exports further adds to the GDP through multiplier effec

Multifocal High-Grade Pancreatic Precursor Lesions: A Case Series and Management Recommendations

Background: The risk of developing invasive cancer in the remnant pancreas after resection of multifocal high-grade pancreatic precursor lesions is not well known. We report three patients who were followed up after resection of multifocal high-grade pancreatic intraepithelial neoplasia (PanIN)-3 or intraductal papillary mucinous neoplasia (IPMN), two of whom eventually developed invasive carcinoma. Presentation: 1) 68-year-old woman who had a laparoscopic distal pancreatectomy for multifocal mixed-type IPMN, identified as high-grade on final pathology, with negative surgical margins. During semiannual monitoring, eight years from the first surgery, the patient developed suspicious features prompting surgical resection of the body with final pathology revealing invasive ductal adenocarcinoma in the setting of IPMN. 2) 48-year-old woman who had a distal pancreatectomy for severe acute/chronic symptomatic pancreatitis, with final pathology revealing multifocal high-grade PanIN-3, with negative surgical margins. Despite semiannual monitoring, two years from the first surgery, the patient developed pancreatic adenocarcinoma with liver metastasis. 3) 55-year-old woman who had a Whipple procedure for symptomatic chronic pancreatitis, with multifocal PanIN-3 on final pathology. The patient underwent completion pancreatectomy due to symptomatology and her high-risk profile, with final pathology confirming multifocal PanIN-3. Conclusion: Multifocal high-grade dysplastic lesions of the pancreas might benefit from surgical resection

Barriers to low carbon retrofit in the domestic built environment

Low carbon retrofit in the domestic built environment is crucial for bringing about a radical environmental and social change in cities. There are around 20 million homes in the UK in need of varying degrees of low carbon and energy efficiency retrofit due to inefficiency. In 2008, UK’s 26 million dwellings were estimated to be responsible for 27% of the country’s total CO2 emissions. 75–85% of the UK’s current building stock will still be in use by 2050. Therefore, improving the energy and carbon performance of existing homes is a major part of dealing with the challenges of climate change, security of energy supply and fuel poverty. The national government and the EU policies have given rise to low carbon retrofitting in the domestic built environment. However, scaling up low carbon retrofit presents a number of barriers from different stakeholders’ perspective involved in the process and understanding the barriers is a key in this journey. This study carried out a systematic review of the existing literature to explore a range of barriers to low carbon retrofit in the domestic built environment. Upfront capital cost, lack of knowledge, interest and time, lack of adequate information and advice, personal behaviour, lack of confidence in suppliers, contractors and technologies, split incentives between landlords and tenants, physical structure of the property, conservation and heritage, inconvenience and disruption and the absence of robust policy and regulatory systems are the major barriers to low carbon domestic retrofit in cities. This study argues that there is a need to address these barriers through effective policy and strategy measures at a national and local level. This may have implications for the design and operation of future low carbon retrofitting in the domestic sector in the UK and abroad

Replicating low carbon smart cities through knowledge sharing and learning across cities: a new approach to urban governance?

Cities are complex urban conurbations and facing various challenges such as increasing urbanization, environmental issues and resource constraints. This makes radical urban innovation an imperative for local government in cities across the world. ‘Smart City’ has emerged as a new concept of urban governance and public administration. Smart city agenda has been gaining attention as a major response to the challenges cities are facing. The European Union (EU) Smart Cities agenda offers new horizons for innovation. EU has invested heavily in the 'Lighthouse Smart Cities', trying to pilot the next generation of low carbon solutions. However, EU does not have sufficient budget to fund all cities for piloting smart city innovation and is keen that cities should learn from Lighthouse Cities and replicate. Sharing knowledge and learning through best practice is paramount in a journey to replicating low carbon smart cities. This is because many projects die after the pilot stage and never scale up. A wide range of innovative initiatives are established in Europe and UK. Unfortunately, up till now, there is little or no cooperation between those initiatives. This is a unique opportunity for cities to share knowledge and use synergies between cross-border initiatives, which can be a new approach to urban governance. Undoubtedly, there is growing need to explore how cities can leverage good practices and smart outcomes in a way that knowledge sharing and lessons learning can be effective to facilitate replication nationally and internationally. Currently, most of the smart city projects are in pilot phases, while academic studies investigating knowledge management and organisational learning perspective for smart cities are far more limited. Besides, most of the new thinking is emerging from practice and is lacking academic rigor suggesting a gap in this area of smart cities. This could be because smart city is mostly deployed as a technological concept and signifies increasing use of digital technologies in designing and delivering products and services in cities. This research aims to explore how can cities share knowledge and learn from each other to facilitate replication of low carbon smart cities? It will explore barriers to knowledge sharing and learning across cities. A framework for replicating low carbon smart cities will be developed for local authorities providing guidelines to cities. The first stage of this research is to conduct comprehensive literature review on low carbon smart cities, knowledge management and organisational learning to develop theoretical underpinning. Based on this, a theoretical model will be developed for conducting empirical research. This research will use mixed-method approach. Qualitative data will be collected with the help of 15-20 semi-structured interviews with managers involved in EU/UK Lighthouse and Follower cities’. Quantitative data will be collected through an online questionnaire and potential respondents will be the individuals involved in smart city projects. Based on the findings, a replication framework will be developed and feedback will be gained from the participants and members of the EU Smart City Network. This study can be useful for local government responsible for implementing smart city innovation

Embedding carbon management in higher education institutions: a journey to sustainable campus

The session aims to explore how higher education institutions can embed carbon management as part of their journey to achieve ‘Sustainable Campus’. Organisational drivers and barriers to implementing carbon management will be discussed. A good practice case study of Nottingham Trent University, UK, will be presented by highlighting its sustainability/carbon management journey. The session will also draw out ‘lessons to be learnt’ from UK universities’ carbon management experience