7,298 research outputs found
Embeddings of graph braid and surface groups in right-angled Artin groups and braid groups
We prove by explicit construction that graph braid groups and most surface
groups can be embedded in a natural way in right-angled Artin groups, and we
point out some consequences of these embedding results. We also show that every
right-angled Artin group can be embedded in a pure surface braid group. On the
other hand, by generalising to right-angled Artin groups a result of Lyndon for
free groups, we show that the Euler characteristic -1 surface group (given by
the relation x^2y^2=z^2) never embeds in a right-angled Artin group.Comment: Published by Algebraic and Geometric Topology at
http://www.maths.warwick.ac.uk/agt/AGTVol4/agt-4-22.abs.htm
To boardrooms and sustainability: the changing nature of segmentation
Market segmentation is the process by which customers in markets with some heterogeneity
are grouped into smaller homogeneous segments of more ‘similar’ customers. A market
segment is a group of individuals, groups or organisations sharing similar characteristics and
buying behaviour that cause them to have relatively similar needs and purchasing behaviour.
Segmentation is not a new concept: for six decades marketers have, in various guises, sought to
break-down a market into sub-groups of users, each sharing common needs, buying behavior
and marketing requirements. However, this approach to target market strategy development
has been rejuvenated in the past few years. Various reasons account for this upsurge in the
usage of segmentation, examination of which forms the focus of this white paper.
Ready access to data enables faster creation of a segmentation and the testing of propositions to
take to market. ‘Big data’ has made the re-thinking of target market segments and value
propositions inevitable, desirable, faster and more flexible. The resulting information has
presented companies with more topical and consumer-generated insights than ever before.
However, many marketers, analytics directors and leadership teams feel over-whelmed by the
sheer quantity and immediacy of such data.
Analytical prowess in consultants and inside client organisations has benefited from a stepchange,
using new heuristics and faster computing power, more topical data and stronger
market insights. The approach to segmentation today is much smarter and has stretched well
away from the days of limited data explored only with cluster analysis. The coverage and wealth
of the solutions are unimaginable when compared to the practices of a few years ago. Then,
typically between only six to ten segments were forced into segmentation solutions, so that an
organisation could cater for these macro segments operationally as well as understand them
intellectually. Now there is the advent of what is commonly recognised as micro segmentation,
where the complexity of business operations and customer management requires highly
granular thinking. In support of this development, traditional agency/consultancy roles have
transitioned into in-house business teams led by data, campaign and business change planners.
The challenge has shifted from developing a granular segmentation solution that describes all
customers and prospects, into one of enabling an organisation to react to the granularity of the
solution, deploying its resources to permit controlled and consistent one-to-one interaction
within segments. So whilst the cost of delivering and maintaining the solution has reduced with
technology advances, a new set of systems, costs and skills in channel and execution
management is required to deliver on this promise. These new capabilities range from rich
feature creative and content management solutions, tailored copy design and deployment tools,
through to instant messaging middleware solutions that initiate multi-streams of activity in a
variety of analytical engines and operational systems.
Companies have recruited analytics and insight teams, often headed by senior personnel, such as
an Insight Manager or Analytics Director. Indeed, the situations-vacant adverts for such
personnel out-weigh posts for brand and marketing managers. Far more companies possess the
in-house expertise necessary to help with segmentation analysis. Some organisations are also
seeking to monetise one of the most regularly under-used latent business assets… data.
Developing the capability and culture to bring data together from all corners of a business, the open market, commercial sources and business partners, is a step-change, often requiring a
Chief Data Officer. This emerging role has also driven the professionalism of data exploration,
using more varied and sophisticated statistical techniques.
CEOs, CFOs and COOs increasingly are the sponsor of segmentation projects as well as the users
of the resulting outputs, rather than CMOs. CEOs because recession has forced re-engineering of
value propositions and the need to look after core customers; CFOs because segmentation leads
to better and more prudent allocation of resources – especially NPD and marketing – around the
most important sub-sets of a market; COOs because they need to better look after key
customers and improve their satisfaction in service delivery. More and more it is recognised that
with a new segmentation comes organisational realignment and change, so most business
functions now have an interest in a segmentation project, not only the marketers.
Largely as a result of the digital era and the growth of analytics, directors and company
leadership teams are becoming used to receiving more extensive market intelligence and
quickly updated customer insight, so leading to faster responses to market changes, customer
issues, competitor moves and their own performance. This refreshing of insight and a leadership
team’s reaction to this intelligence often result in there being more frequent modification of a
target market strategy and segmentation decisions.
So many projects set up to consider multi-channel strategy and offerings; digital marketing;
customer relationship management; brand strategies; new product and service development;
the re-thinking of value propositions, and so forth, now routinely commence with a
segmentation piece in order to frame the ongoing work. Most organisations have deployed
CRM systems and harnessed associated customer data. CRM first requires clarity in segment
priorities. The insights from a CRM system help inform the segmentation agenda and steer how
they engage with their important customers or prospects. The growth of CRM and its ensuing
data have assisted the ongoing deployment of segmentation.
One of the biggest changes for segmentation is the extent to which it is now deployed by
practitioners in the public and not-for-profit sectors, who are harnessing what is termed social
marketing, in order to develop and to execute more shrewdly their targeting, campaigns and
messaging. For Marketing per se, the interest in the marketing toolkit from non-profit
organisations, has been big news in recent years. At the very heart of the concept of social
marketing is the market segmentation process.
The extreme rise in the threat to security from global unrest, terrorism and crime has focused
the minds of governments, security chiefs and their advisors. As a result, significant resources,
intellectual capability, computing and data management have been brought to bear on the
problem. The core of this work is the importance of identifying and profiling threats and so
mitigating risk. In practice, much of this security and surveillance work harnesses the tools
developed for market segmentation and the profiling of different consumer behaviours.
This white paper presents the findings from interviews with leading exponents of segmentation
and also the insights from a recent study of marketing practitioners relating to their current
imperatives and foci. More extensive views of some of these ‘leading lights’ have been sought
and are included here in order to showcase the latest developments and to help explain both
the ongoing surge of segmentation and the issues under-pinning its practice. The principal
trends and developments are thereby presented and discussed in this paper
Residually free 3-manifolds
We classify those compact 3-manifolds with incompressible toral boundary
whose fundamental groups are residually free. For example, if such a manifold
is prime and orientable and the fundamental group of is non-trivial
then , where is a surface.Comment: 19 pages, referee's comments incorporated, to appear in Algebraic &
Geometric Topolog
Long range financial data and model choice
Long range financial data as typified by the daily returns of the Standard and Poor's index exhibit common features such as heavy tails, long range memory of the absolute values and clustering of periods of high and low volatility. These and other features are often referred to as stylized facts and parametric models for such data are required to reproduce them in some sense. Typically this is done by simulating some data sets under the model and demonstrating that the simulations also exhibits the stylized facts. Nevertheless when the parameters of such models are to be estimated recourse is very often taken to likelihood either in the form of maximum likelihood or Bayes. In this paper we expound a method of determining parameter values which depends solely on the ability of the model to reproduce the relevant features of the data set. We introduce a new measure of the volatility of the volatility and show how it can be combined with the distribution of the returns and the autocorrelation of the absolute returns to determine parameter values. We also give a parametric model for such data and show that it can reproduce the required features. --
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Television and the future internet: the NoTube project
[1st paragraph] 'New technology is transforming the TV industry', Mark Thompson, BBC Director General told the newspaper The Observer. The classic notion of TV being a set in the living room with finite channels and linear programming is already gone: TV has moved into the world of Internet and mobile technology and content is growing exponentially in terms of number and diversity. The notion of channels is being replaced by individual choice and on-demand programming. Distinctions between TV and other streaming content are blurred: both live in a shared connected online world. We expect that as the Future Internet develops, TV will complete this disruptive paradigm shift into becoming ubiquituous, always-available, and increasingly personalized. NoTube is a EU funded project (in the Objective 4.3 Intelligent Information Management) which began February 2009 and runs for three years, with the goal to prepare TV for the Future Internet – addressing challenges of TV content ubiquity and choice, personalization and integration
Presenting parabolic subgroups
Consider a relatively hyperbolic group G. We prove that if G is finitely
presented, so are its parabolic subgroups. Moreover, a presentation of the
parabolic subgroups can be found algorithmically from a presentation of G, a
solution of its word problem, and generating sets of the parabolic subgroups.
We also give an algorithm that finds parabolic subgroups in a given recursively
enumerable class of groups.Comment: 15 page
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