BAYESIAN ANALYSIS OF THE COMPOUND COLLECTIVE MODEL: THE NET PREMIUM PRINCIPLE WITH EXPONENTIAL POISSON AND GAMMA–GAMMA DISTRIBUTIONS

This article develops a Bayesian analysis of the Compound Collective Model utilizing the Net Premium Principle, considering single-period models. With respect to likelihoods, we used a Poisson distribution for the number of claims and an Exponential distribution for the severity of the accident/event. Gamma distributions were used for the prior distributions. The robustness of the posterior premium was analyzed with respect to the prior distribution specification of the severity of the accident/event, utilizing contamination classes, these being the class of all the distributions and that of all the unimodal distributions with the same mode. Numerical applications of the results obtained were performed.Compound collective model; Bayesian analysis; Robustness analysis.

The Weevil Next Door: Exploring the impact of associational effects on C. pitcheri to better biological control practices

Lake Michigan dwelling dune thistle, Circium pitcheri, is a federally threatened plant, whose reproduction is affected by a non-native weevil, Larinus planus. Originally introduced as a biological control agent to combat the spread of Canada thistle, Circium arvense, this weevil is instead using C. pitcheri as a host for its larvae. Associational susceptibility is an important factor to consider in hopes of preventing the damage to this endangered plant. The goal of this study was to observe L. planus behavior to determine why there is a correlation between increased density of beach grass and high levels of C. pitcheri damage. We hypothesize that C. pitcheri’s neighboring grass community is used as a dispersal aid for the non-native weevil, making neighboring thistle hosts more susceptible to weevil damage in grassy environments. To test this, we conducted ethogram studies at Whitefish Dunes State Park (WDSP) in Door County, WI. At WDSP, we found that L. planus physically used beach grass to get to C. pitcheri and largely failed to disperse using the sand. These results should help provide ecologically sustainable management strategies, while also promote more in-depth host specific analyses prior to the release of biological control agents

A Ball in a Groove

We study the static equilibrium of an elastic sphere held in a rigid groove by gravity and frictional contacts, as determined by contact mechanics. As a function of the opening angle of the groove and the tilt of the groove with respect to the vertical, we identify two regimes of static equilibrium for the ball. In the first of these, at large opening angle or low tilt, the ball rolls at both contacts as it is loaded. This is an analog of the "elastic" regime in the mechanics of granular media. At smaller opening angles or larger tilts, the ball rolls at one contact and slides at the other as it is loaded, analogously with the "plastic" regime in the mechanics of granular media. In the elastic regime, the stress indeterminacy is resolved by the underlying kinetics of the ball response to loading.Comment: RevTeX 3.0, 4 pages, 2 eps figures included with eps

The SME Drag Effect in the West Midlands Economy

Our main objective is to highlight that deeper and targeted investigation of the development and growth of SMEs in particular regions might facilitate policy development that drives SME growth. With this in mind, we have produced three reports, of which this is the first. This report focuses on the key economic data on the West Midlands in the last twenty years with the main objective of providing an analysis of the SME economy in the West Midlands with a particular focus on the Greater Birmingham and Solihull Local Enterprise Partnership (GBSLEP) and Black Country Local Enterprise Partnership (BCLEP). Our findings show that in the last five years whilst the West Midlands’ was experiencing prospering economic growth prospects the SME part of the economy was experiencing a ‘drag effect’ . Our analysis highlights a flourishing West Midlands economy since the 2008 Global Financial Crisis (GFC). However, a detailed look at the SME data displays an intensifying low set of productivity levels in the region’s SME economy indicating that the West Midlands economy does not necessarily operate at its full potential. Despite the improving productivity levels in the West Midlands since 2012, the productivity levels of GBSLEP lagged significantly behind the West Midlands productivity levels until 2016. Oscillations in the productivity levels of BCLEP has been commonplace since 2008 GFC. We postulate the differences in the productivity patterns of GBSLEP and BCLEP might be due to the changes in their industrial structure, in the characteristics of SMEs and in the targeted SME policies: • A regional productivity analysis by ONS (2018a) substantiates the West Midlands being the only region with an SME drag effect due to a contrasting relationship between industry structure and firm productivity. The changes to the industry structure positively affect the region’s productivity levels, yet it is not large enough to compensate for the effect of the low average firm productivity levels. • We observe a deepening productivity problem in micro and small enterprises in the West Midlands more than any other firm category. • The West Midlands’ share of HGFs is below the UK average and fluctuating from year to year without ensuring a steady impact on productivity. The share of HGFs in GBSLEP and BCLEP continues to fall as opposed to a recovery, as would be expected from the targeted policies these firms received. We recommend that reducing the SME drag effect on the West Midlands economy can be achieved by shifting attention to SMEs that grow 5-20% annually and/or over the three years

Transformation Triangle for SME Productivity and Growth

In the aftermath of the Covid-19 pandemic, Brexit and an economic trajectory of soaring energy prices, supply chain problems, labour shortages, increasing inflation and interest rates there is great urgency in focussing on how we can help SMEs to build their productivity and growth. In other words, in an era of limited resources, how can we design/reshape business support mechanisms (in the form of strategies, practices, new areas of supports) that are relevant to the changing economic, social and environmental context of SMEs? While enacting business support is a comprehensive activity that involves several agents within the economy, the starting point is to develop a sound business support policy which fully understands growth. Such a policy can be devised in the light of a conceptual framework which is developed not only through academic expertise but also through combining practitioner insights and experiences. In this paper, we develop a comprehensive growth framework for SMEs called the ‘Transformation Triangle’ that aims to bridge the gap between empirical evidence and practice. To do so, we build on our extensive empirical research combined with our own engaged scholarship activities with SMEs. Our empirical evidence derives from our extensive analysis of the West Midlands SMEs. Firstly, we conducted a secondary data analysis of the West Midlands economy in the last twenty years. Secondly, we analysed primary data collected through our Promoting Sustainable Performance (PSP) project - a comprehensive business diagnostic survey which was completed by 291 West Midlands SMEs prior to March 2020. Throughout the same period, one of our authors was involved directly with the SMEs in terms of a facilitated diagnostic and one-to-one interventions to develop a business strategy which aimed to address the main/idiosyncratic problems of the issues identified through our PSP diagnostic tool. Our engaged scholarship activity shed light into the emerging issues in the SME environment prior to and throughout the Covid pandemic. Insights are integrated into the development of our framework of the ‘Transformation Triangle’. The extensive analysis of key economic data on SMEs in West Midlands helped us identify a paradox that was happening in the West Midlands economy up until the start of the Covid-19 pandemic: We call it the ‘SME drag effect’ on the burgeoning West Midlands’ economic growth since 2012.[1] We showed that while the West Midlands is among the few regions in England (with London and East England) to successfully surpass the adverse economic impact of 2008 Global Financial Crisis (GFC), it has nonetheless continued to suffer productivity problems due to an unhealthy balance between positive but small size industry-mix effects on productivity and large and negative effects of firm-level productivity (ONS 2018).[2] Our findings indicated that the shift from production to services sector in the last twenty years might have contributed to improving the West Midlands’ economy, but in terms of productivity, the outcome is not so conclusive. Our findings also established the link between low firm productivity in the West Midlands and the SME economy (i.e. the latter being less productive than it could have been), which called for an exploration of the shortcomings within the SME sector that might cause this drag effect. We distinguished the underlying reasons behind the SME drag effect in the West Midlands by analysing our primary data through bivariate and econometric analysis of four groups of SMEs, namely high growth, low growth, static and declining, against a wide range of indicators that emerge out of multiple academic disciplines and, hence, range from management and strategy, external relations, innovation and technology, human resource and knowledge management.[3] Our findings largely indicate that: 1. the differences in the way SME managers perceive and influence the business operations and strategies not only affect their level of growth but also leave no room for change, 2. the fact that most businesses do not have a full understanding of strategy becomes an obstacle for successful organisational transformation that could pave the way for an increase in efficiency and productivity, 3. under-investment in technology and a lack of understanding how to implement new digital technologies holds back the majority of SMEs from becoming higher growth SMEs that will otherwise help to improve business productivity and growth in the SME sector. These findings shed light on the pre-pandemic situation of the SME sector, and when combined with the unprecedented disruption that the pandemic imposed on to the businesses, they point to a clear necessity for a new approach to supporting SMEs that encapsulates both (i) the need for a change at various levels (i.e. entrepreneur, owner/manager, employee and/or organisational) that were already starting to emerge before the pandemic (e.g. in relation to strategy development, growth aspirations, approach to human resources, etc.) and (ii) the new business environment the pandemic has enforced on the businesses (e.g. integration of digital technologies into business operations, responding to calls for sustainability, circular economy in their businesses). Therefore, we build a transformation approach to SME productivity and growth on the inference from the pre-Covid data on SMEs and link it to the imminent developments of the Covid-19 pandemic. The framework we generate in this paper sets out to address this need in order to overcome the SME drag effect by focussing on the transformational effect of three areas, which are mindset transformation, strategic transformation and digital transformation. The interdependent but dynamic relationships between these three areas are framed through what we call a ‘Transformation Triangle’ to achieve and sustain SME productivity and growth. The triangle is composed of 1. transformation of business strategy development, as strategy is at the core of firm growth, 2. transformation of mindsets to enable the ability to overcome barriers and transition to different stages of innovation and growth 3. the adoption of digital technologies, which constitute the technological paradigm of a new industrial revolution that cannot be ignored by any size of business. The third process in this framework is a fluid one, as it will be replaced with new paradigms as they emerge. For instance, once digital transformation is successfully achieved, SMEs can address green transformation with net-zero economy goals. While these emerging paradigms seem be at their infancy and rather far away goals at the moment, businesses can soon find themselves as laggards if they do not initiate a timely planning and gradual implementation process for it. Our framework aims at not only balancing the trade-off between short term and long term approaches to strategic management but also accentuating/calling attention to the covert aspects of SME growth that are pertinent to endorsing strategic management but largely overlooked. It is, however, not a temporary response to the Covid crisis, rather it provides a systematic approach to organisational transformation that forward-looking SMEs can adopt not only to survive but also to emerge out of the Covid crisis ready to grow. A successful implementation of ‘Transformation Triangle’ by the SMEs supported by the targeted SME policies in these areas by the local and national governments promises creating higher productivity and sustainable regional and national economies. Therefore, we believe it will be evermore useful to SMEs and policymakers as a new tool in the aftermath of Covid-19 pandemic. This paper will explain each node of the Transformation Triangle in detail and show how SMEs, policymakers and practitioners can utilise our framework for building increased productivity and growth in the 21st century. [1] For the detailed analysis of the origins and the conceptualisation of the drag effect of SMEs in the West Midlands, see Yoruk, D.E. and Gilman, M., (2021a). “The SME Drag Effect in the West Midlands Economy”, Birmingham City Business School, Centre for Enterprise, Innovation and Growth, CEIG Report No.1/2021. [2] Office for National Statistics (2018), ‘The regional firm-level productivity analysis for the non-financial business economy, Great Britain, April 2018’. While Scotland presents a similar trend, as opposed to Scotland, in the West Midlands the rising productivity level due to the changing industry structure is not sufficient to reverse the drag effect created by the low firm-level productivity. [3] Yoruk, D.E. and M. Gilman (2021b), “Understanding the SME Drag Effect in the West Midlands Economy – Findings of PSP Growth Diagnostic (Survey)”, Birmingham City Business School, Centre for Enterprise, Innovation and Growth, CEIG Report No.2/2021

Understanding the SME Drag Effect in the West Midlands Economy – Findings of PSP Growth Diagnostic (Survey)

This report provides an in-depth analysis of the SME economy in the Greater Birmingham and Solihull Local Enterprise Partnership (GBSLEP) and Black Country Local Enterprise Partnership (BCLEP) with the main objective of enhancing our understanding of the reasons behind the SME drag effect on the West Midlands economy. This report uses data from our own Promoting Sustainable Performance (PSP) survey (see Appendix A for details of this methodology) conducted between March 2018 and March 2020. We investigated a sample of SMEs operating in GBSLEP and BCLEP economies with respect to their growth and wider business activities. We compared four SME growth classifications, namely high growth firms (HGFs), low growth firms (LGFs), static firms (SFs), and declining firms (DFs). Our findings show that • Future growth aspirations are not systematically supported by structured reflection, learning, planning and strategy. • A general lack of understanding of strategic management by the owner-managers manifests in a strong reliance on managing the business on their own rather than involving other specialised people in business operations, substituting accounting-related measures for strategic measures for performance, and confusing having a business plan with having a business strategy. • An excessive and short-term focus on sales and marketing strategies is at the core of SME management priorities. However, high growth is more likely when a long-term perspective in developing value-creating relations with customers & suppliers is pursued and when SMEs undertake strategic investments in technology acquisition and human resources. • While product or service differentiation or finding a niche is a recipe for SME growth, when complemented with cost leadership strategies, it leads to high/rapid growth, as the latter stimulate achieving higher productivity (e.g. through more process innovation and the use of technology). • Growth is more likely when employees become a source of competitive advantage, which in turn helps overcome productivity problem. However, SMEs are less likely to communicate their strategies with their employees, to invest in hiring qualified skilled employees and in training their existing employees. • Growth is more likely when information and advice are sought strategically. It is not only about the kinds of information and advice SMEs seek but also about how they operationalise this information and advice through their business strategy (i.e. leveraging their capabilities). Our analysis of the SME growth classifications detects that DFs purport to utilise similar practices and strategies to HGFs but it does not necessarily deliver growth. This result highlights that in order to successfully implement the strategies of HGFs, the firm needs a proper understanding of business strategy development and structured purposeful planning. Moreover, this understanding needs to be complemented with capability development within the firm. This holds regardless of the sector an SME is operating in. We recommend that in a business environment shaped by the Covid-19 pandemic, policies need to consider accommodating the needs of a wider variety of SMEs (i.e. not only HGFs) both for survival and growth through improved productivity and efficiency. For this, a new approach to SME development and growth needs to be adopted by SME owner-managers and the local authorities, which will be elaborated on in our third report

Lateral Separation of Macromolecules and Polyelectrolytes in Microlithographic Arrays

A new approach to separation of a variety of microscopic and mesoscopic objects in dilute solution is presented. The approach takes advantage of unique properties of a specially designed separation device (sieve), which can be readily built using already developed microlithographic techniques. Due to the broken reflection symmetry in its design, the direction of motion of an object in the sieve varies as a function of its self-diffusion constant, causing separation transverse to its direction of motion. This gives the device some significant and unique advantages over existing fractionation methods based on centrifugation and electrophoresis.Comment: 4 pages with 3 eps figures, needs RevTeX 3.0 and epsf, also available in postscript form http://cmtw.harvard.edu/~deniz

Case Report: Behavioral Disorder Following Hemispherotomy: A Valproate Effect?

Background: Hemispherotomy is an epilepsy surgery procedure applied to cure particularly pharmacorefractory lesional epilepsy due to unihemispheric pathologies. Such a disconnection of an entire hemisphere is followed by reorganizational processes. Methods: We describe an acute aggravation of behavioral problems following a hemispherotomy in a patient treated with valproic acid, which subsided once valproate was discontinued. Results: A 9-year-old boy with drug-resistant epilepsy caused by the residua of a perinatal stroke treated for several years with valproic acid and lamotrigine underwent hemispherotomy. Shortly after surgery, minimal preoperative behavioral problems intensified dramatically, and aggression occurred as a new symptom. Assuming a correlation between valproate treatment and the postoperative altered neuronal network, we tapered off valproate. The behavioral problems decreased in intensity with the reduction of valproate dose and disappeared after drug discontinuation. Conclusion: We describe severe behavioral problems after hemispherotomy that subsided when valproate was tapered off. While we cannot rule out a spontaneous correction of a post-hemispherotomy network dysregulation, our report raises awareness to possible altered effects of the anticonvulsant valproic acid parallel to reorganizational processes after hemispherotomy

Randomly Charged Polymers, Random Walks, and Their Extremal Properties

Motivated by an investigation of ground state properties of randomly charged polymers, we discuss the size distribution of the largest Q-segments (segments with total charge Q) in such N-mers. Upon mapping the charge sequence to one--dimensional random walks (RWs), this corresponds to finding the probability for the largest segment with total displacement Q in an N-step RW to have length L. Using analytical, exact enumeration, and Monte Carlo methods, we reveal the complex structure of the probability distribution in the large N limit. In particular, the size of the longest neutral segment has a distribution with a square-root singularity at l=L/N=1, an essential singularity at l=0, and a discontinuous derivative at l=1/2. The behavior near l=1 is related to a another interesting RW problem which we call the "staircase problem". We also discuss the generalized problem for d-dimensional RWs.Comment: 33 pages, 19 Postscript figures, RevTe