Concentration of norms and eigenvalues of random matrices

We prove concentration results for $\ell_p^n$ operator norms of rectangular random matrices and eigenvalues of self-adjoint random matrices. The random matrices we consider have bounded entries which are independent, up to a possible self-adjointness constraint. Our results are based on an isoperimetric inequality for product spaces due to Talagrand.Comment: 15 pages; AMS-LaTeX; updated one referenc

Recognizing Interspersed sketches quickly

Sketch recognition is the automated recognition of hand-drawn diagrams. When allowing users to sketch as they would naturally, users may draw shapes in an interspersed manner, starting a second shape before finishing the first. In order to provide freedom to draw interspersed shapes, an exponential combination of subshapes must be considered. Because of this, most sketch recognition systems either choose not to handle interspersing, or handle only a limited pre-defined amount of interspersing. Our goal is to eliminate such interspersing drawing constraints from the sketcher. This paper presents a high-level recognition algorithm that, while still exponential, allows for complete interspersing freedom, running in near real-time through early effective sub-tree pruning. At the core of the algorithm is an indexing technique that takes advantage of geometric sketch recognition techniques to index each shape for efficient access and fast pruning during recognition. We have stresstested our algorithm to show that the system recognizes shapes in less than a second even with over a hundred candidate subshapes on screen.National Science Foundation (U.S.) (IIS Creative IT Grant #0757557

Creating the Perception-based LADDER sketch recognition language

Sketch recognition is automated understanding of hand-drawn diagrams. Current sketch recognition systems exist for only a handful of domains, which contain on the order of 10--20 shapes. Our goal was to create a generalized method for recognition that could work for many domains, increasing the number of shapes that could be recognized in real-time, while maintaining a high accuracy. In an effort to effectively recognize shapes while allowing drawing freedom (both drawing-style freedom and perceptually-valid variations), we created the shape description language modeled after the way people naturally describe shapes to 1) create an intuitive and easy to understand description, providing transparency to the underlying recognition process, and 2) to improve recognition by providing recognition flexibility (drawing freedom) that is aligned with how humans perceive shapes. This paper describes the results of a study performed to see how users naturally describe shapes. A sample of 35 subjects described or drew approximately 16 shapes each. Results show a common vocabulary related to Gestalt grouping and singularities. Results also show that perception, similarity, and context play an important role in how people describe shapes. This study resulted in a language (LADDER) that allows shape recognizers for any domain to be automatically generated from a single hand-drawn example of each shape. Sketch systems for over 30 different domains have been automatically generated based on this language. The largest domain contained 923 distinct shapes, and achieved a recognition accuracy of 83% (and a top-3 accuracy of 87%) on a corpus of over 11,000 sketches, which recognizes almost two orders of magnitude more shapes than any other existing system.National Science Foundation (U.S.) (grant 0757557)National Science Foundation (U.S.) (grant 0943499

Parents’ perspectives and experiences of parenting and caring for young children on a low income in the North East Scotland.

Background: Families with young children, and lone parent families in particular, are at greater risk of poverty and food insecurity, compared to other UK population groups. Tackling child poverty has been a key Scottish Government policy since the introduction of the Child Poverty Act (2017) in which local authorities and health boards are required to report on their Local Child Poverty Action Plans. In north east Scotland little formal research had focused on the lived experiences of parents and parents of infants and young children in relation to the challenges they face parenting on very low incomes, and, on questions about income maximisation strategies to alleviate child poverty. This paper focuses on some key findings of a study undertaken to address this knowledge gap in Grampian in 2020. Methods: Parents with young children supported by an Aberdeen City-based poverty alleviation social enterprise were invited to take part in an interview study. One-to-one semi-structured telephone interviews lasting between 30–40 minutes took place during July and August 2020. Interviews were transcribed and thematically analysed. Results: Ten women took part; two participants lived with partners. Eight participants were unemployed and two worked part-time. Each had between one and five child(ren), and all had one child under school-age. Five key impact themes emerged, i. limited participation in paid employment; ii. insufficient social security income; iii. household food insecurity experiences; iv. practical and emotional challenges and anxiety associated with their children’s overall development; and v. anxieties related to treats and special occasions. Four coping strategy themes were also revealed, i.e. i. budgeting and bill prioritisation; ii. self-sacrifice; iii. relying on others, and iv. keeping up appearances. Food coping strategies were explored in more depth, and two broad themes emerged: acquisition methods and management techniques. Discussion: Parents with young children experience significant barriers accessing paid employment due to caring responsibilities. Consequently, generating sufficient household income from alternate income sources, such as social security, is problematic. Parents reported devoting significant emotional and physical energy to dealing with the challenges of raising children in poverty, and it was notable that participants employed a range of sophisticated coping strategies and skill to make ends meet and maximise food resources, within highly constrained budgets. This research challenges notions that budgeting education initiatives have much to offer low income parents already well-versed on this issue. Strategies to increase their incomes seem a more effective way of alleviating their related anxieties

Low income parents’ perspectives and experiences of engaging with early years health professionals about financial challenges and income maximisation.

Background: Since the introduction of the Child Poverty Act (2017) in Scotland, all health visitors, midwives and family nurses in Scotland are expected to screen and offer a financial advice referral to at-risk pregnant women and parents/carers of families with children under five in Scotland. The so-called ‘Financial Inclusion Pathway’(FIP) emerged in 2019 as one of a number of strategies intended to tackle child poverty. At this early implementation stage, little is known about parents’ perspectives about the acceptability or impact of this initiative in relation to its aim. Methods: In 2020, low income parents with young children living in Aberdeen City were invited to take part in a qualitative study that aimed to determine any challenges they might face engaging with the FIP policy in practice, and their perspectives about financial discussions with professionals that could help to increase household incomes through this approach. One-to-one semi-structured telephone interviews lasting between 30–40 minutes took place during July and August 2020. Interviews were fully transcribed and thematically analysed. Results: Ten women, ranging from ages 20–41 years. Each participant had between one and five child(ren), ranging in age from 2 to 18 years and all had one child under school-age. All lived in multiply deprived postcode areas within Aberdeen City. Three main themes emerged: i. difficulties associated with discussing financial concerns; ii. how to talk about the issue; iii. intervention utility. Within each of these three main themes, nine-sub themes were apparent, ranging from those indicating potential unintended negative consequences, as well as intervention benefits. Discussion: Most participants considered health visitors to be a potentially good source of help about financial challenges; they were less clear about midwives’ role here. However, parents’ perceptions of the problems they may face associated with disclosing financial difficulties to health professionals, is a distinct barrier to conversations that could lead to a financial advice referral. Given the levels of unclaimed benefit in the UK, this is important to note. Establishing trust and rapport, careful and sensitive enquiry, and positive framing of financial maximisation were recommended to aid discussion of financial challenges. These findings are important given the current and predicted economic impact of the COVID-19. The study is limited by its sample size and recruitment site, but provides valuable insights to inform a larger scale investigation. The study also indicates the importance of understanding health professionals’ associated views and experiences