Balancing Bounded Treewidth Circuits

Algorithmic tools for graphs of small treewidth are used to address questions in complexity theory. For both arithmetic and Boolean circuits, it is shown that any circuit of size $n^{O(1)}$ and treewidth $O(\log^i n)$ can be simulated by a circuit of width $O(\log^{i+1} n)$ and size $n^c$, where $c = O(1)$, if $i=0$, and $c=O(\log \log n)$ otherwise. For our main construction, we prove that multiplicatively disjoint arithmetic circuits of size $n^{O(1)}$ and treewidth $k$ can be simulated by bounded fan-in arithmetic formulas of depth $O(k^2\log n)$. From this we derive the analogous statement for syntactically multilinear arithmetic circuits, which strengthens a theorem of Mahajan and Rao. As another application, we derive that constant width arithmetic circuits of size $n^{O(1)}$ can be balanced to depth $O(\log n)$, provided certain restrictions are made on the use of iterated multiplication. Also from our main construction, we derive that Boolean bounded fan-in circuits of size $n^{O(1)}$ and treewidth $k$ can be simulated by bounded fan-in formulas of depth $O(k^2\log n)$. This strengthens in the non-uniform setting the known inclusion that $SC^0 \subseteq NC^1$. Finally, we apply our construction to show that {\sc reachability} for directed graphs of bounded treewidth is in $LogDCFL$

Fast Breadth-First Search in Still Less Space

It is shown that a breadth-first search in a directed or undirected graph with $n$ vertices and $m$ edges can be carried out in $O(n+m)$ time with $n\log_2 3+O((\log n)^2)$ bits of working memory

Computing with and without arbitrary large numbers

In the study of random access machines (RAMs) it has been shown that the availability of an extra input integer, having no special properties other than being sufficiently large, is enough to reduce the computational complexity of some problems. However, this has only been shown so far for specific problems. We provide a characterization of the power of such extra inputs for general problems. To do so, we first correct a classical result by Simon and Szegedy (1992) as well as one by Simon (1981). In the former we show mistakes in the proof and correct these by an entirely new construction, with no great change to the results. In the latter, the original proof direction stands with only minor modifications, but the new results are far stronger than those of Simon (1981). In both cases, the new constructions provide the theoretical tools required to characterize the power of arbitrary large numbers.Comment: 12 pages (main text) + 30 pages (appendices), 1 figure. Extended abstract. The full paper was presented at TAMC 2013. (Reference given is for the paper version, as it appears in the proceedings.

Computing with cells: membrane systems - some complexity issues.

Membrane computing is a branch of natural computing which abstracts computing models from the structure and the functioning of the living cell. The main ingredients of membrane systems, called P systems, are (i) the membrane structure, which consists of a hierarchical arrangements of membranes which delimit compartments where (ii) multisets of symbols, called objects, evolve according to (iii) sets of rules which are localised and associated with compartments. By using the rules in a nondeterministic/deterministic maximally parallel manner, transitions between the system configurations can be obtained. A sequence of transitions is a computation of how the system is evolving. Various ways of controlling the transfer of objects from one membrane to another and applying the rules, as well as possibilities to dissolve, divide or create membranes have been studied. Membrane systems have a great potential for implementing massively concurrent systems in an efficient way that would allow us to solve currently intractable problems once future biotechnology gives way to a practical bio-realization. In this paper we survey some interesting and fundamental complexity issues such as universality vs. nonuniversality, determinism vs. nondeterminism, membrane and alphabet size hierarchies, characterizations of context-sensitive languages and other language classes and various notions of parallelism

Information needs after stroke: What to include and how to structure it on a website. A qualitative study using focus groups and card sorting

Background: Use of the Internet to obtain health and other information is increasing. Previous studies have identified the specific information needs of people with stroke but not in relation to the Internet. People with aphasia (PwA) may face barriers in accessing the Internet: Navigating websites requires an ability to categorise information and this ability is often impaired in PwA. The website categorisation preferences of people with stroke and with aphasia have not yet been reported. Aims: This study aimed: (a) to determine what information people who have had a stroke would like to see on a website about living with stroke; (b) to determine the most effective means of structuring information on the website so that it is accessible to people with stroke; and c) to identify any differences between people with and without aphasia in terms of preferences for structuring information on the website. Methods & Procedures: Participants were recruited from a hospital's Stroke Database. Focus groups were used to elicit what information participants wanted on a website about living with stroke. The themes raised were depicted on 133 cards. To determine the most effective way of structuring information on the website, and whether there were any differences in preferences between PwA and PwoA, participants used a modified closed card-sorting technique to sort the cards under website categories. Outcomes & Results: A total of 48 people were invited, and 12 (25%) agreed to take part. We ran three focus groups: one with PwA (n = 5) and two with people without aphasia (PwoA) (n = 3, n = 4). Participants wanted more information about stroke causes and effects (particularly emotional issues), roles of local agencies, and returning to previous activities (driving, going out). All participants completed the card-sorting exercise. Few cards (6%) were categorised identically by everyone. Cards relating to local agencies and groups were not consistently categorised together. Cards relating to emotions were segregated. The categorisation preferences for PwA were more fragmented than those for PwoA: 60% of PwA agreed on the categorisation of 51% of the cards, whereas 60% of PwoA agreed on the categorisation of 76% of the cards. Conclusions: Information needs covered all stages of the stroke journey. The card sorting was accessible to everyone, and provided evidence of structuring preferences and of some of the categorisation difficulties faced by PwA. More research is needed on what an accessible website looks like for PwA

Scenario planning for the Edinburgh city region

This paper examines the application of scenario planning techniques to the detailed and daunting challenge of city re-positioning when policy makers are faced with a heavy history and a complex future context. It reviews a process of scenario planning undertaken in the Edinburgh city region, exploring the scenario process and its contribution to strategies and policies for city repositioning. Strongly rooted in the recent literature on urban and regional economic development, the text outlines how key individuals and organisations involved in the process participated in far-reaching analyses of the possible future worlds in which the Edinburgh city region might find itself

Derandomized Squaring of Graphs

We introduce a “derandomized ” analogue of graph squaring. This op-eration increases the connectivity of the graph (as measured by the second eigenvalue) almost as well as squaring the graph does, yet only increases the degree of the graph by a constant factor, instead of squaring the degree. One application of this product is an alternative proof of Reingold’s re-cent breakthrough result that S-T Connectivity in Undirected Graphs can be solved in deterministic logspace.

Exploring good practice in life story work with people with dementia : the findings of a qualitative study looking at the multiple views of stakeholders

Introduction: Despite growing international interest in life story work as a tool for person-centred dementia care, there is little agreement on what constitutes good practice and little evidence from the perspectives of people with dementia or their family carers. Design and methods: This paper reports the findings from the qualitative element of a larger study looking at the feasibility of evaluating life story work. Ten focus groups were held with 73 participants: four groups of people with dementia (25 participants), three with family carers (21 participants), and three with staff, professionals and volunteers with experience of life story work (27 participants). Findings: It became apparent through our focus groups that, when people talk about ‘life story work’, different people mean different things. This related to both process and outcomes. In particular, a person with dementia may have very different views from others about what life story work is for and how their life story products should be used. There was general agreement that a good practice approach would be tailored to the individual needs and preferences of the person with dementia. However, in practice many settings used templates and the process was led by staff or completed by family carers. Conclusion: We produced nine key features of good practice which could be used to guide the life story work process. Key elements include: the recognition that not everyone will want to take part in life story work and that some people may even find it distressing; the importance of being led by the person with dementia themselves; the need for training and support for staff, carers and volunteers; and the potential for life story work to celebrate the person’s life today and look to the future

The Impact of Dementia on Women Internationally: an Integrative Review

Women are disproportionately affected by dementia, both in terms of developing dementia and becoming caregivers. We conducted an integrative review of English language literature of the issues affecting women in relation to dementia from an international perspective. The majority of relevant studies were conducted in high income countries, and none were from low-income countries. The effects of caregiving on health, wellbeing and finances are greater for women; issues facing women, particularly in low and middle-income countries need to be better understood. Research should focus on building resilience to help people adjust and cope long term

Space Complexity of the Directed Reachability Problem over Surface-Embedded Graphs

The graph reachability problem, the computational task of deciding whether there is a path between two given nodes in a graph is the canonical problem for studying space bounded computations. Three central open questions regarding the space complexity of the reachabil-ity problem over directed graphs are: (1) improving Savitch’s O(log2 n) space bound, (2) designing a polynomial-time algorithm with O(n1−) space bound, and (3) designing an unambiguous non-deterministic log-space (UL) algorithm. These are well-known open questions in complex-ity theory, and solving any one of them will be a major breakthrough. We will discuss some of the recent progress reported on these questions for certain subclasses of surface-embedded directed graphs