Fully Dynamic Matching in Bipartite Graphs

Maximum cardinality matching in bipartite graphs is an important and well-studied problem. The fully dynamic version, in which edges are inserted and deleted over time has also been the subject of much attention. Existing algorithms for dynamic matching (in general graphs) seem to fall into two groups: there are fast (mostly randomized) algorithms that do not achieve a better than 2-approximation, and there slow algorithms with \O(\sqrt{m}) update time that achieve a better-than-2 approximation. Thus the obvious question is whether we can design an algorithm -- deterministic or randomized -- that achieves a tradeoff between these two: a $o(\sqrt{m})$ approximation and a better-than-2 approximation simultaneously. We answer this question in the affirmative for bipartite graphs. Our main result is a fully dynamic algorithm that maintains a 3/2 + \eps approximation in worst-case update time O(m^{1/4}\eps^{/2.5}). We also give stronger results for graphs whose arboricity is at most \al, achieving a (1+ \eps) approximation in worst-case time O(\al (\al + \log n)) for constant \eps. When the arboricity is constant, this bound is $O(\log n)$ and when the arboricity is polylogarithmic the update time is also polylogarithmic. The most important technical developement is the use of an intermediate graph we call an edge degree constrained subgraph (EDCS). This graph places constraints on the sum of the degrees of the endpoints of each edge: upper bounds for matched edges and lower bounds for unmatched edges. The main technical content of our paper involves showing both how to maintain an EDCS dynamically and that and EDCS always contains a sufficiently large matching. We also make use of graph orientations to help bound the amount of work done during each update.Comment: Longer version of paper that appears in ICALP 201

Discrete Time from Quantum Physics

't Hooft has recently developed a discretisation of (2+1) gravity which has a multiple-valued Hamiltonian and which therefore admits quantum time evolution only in discrete steps. In this paper, we describe several models in the continuum with single-valued equations of motion in classical physics, but with multiple-valued Hamiltonians. Their time displacements in quantum theory are therefore obliged to be discrete. Classical models on smooth spatial manifolds are also constructed with the property that spatial displacements can be implemented only in discrete steps in quantum theory. All these models show that quantization can profoundly affect classical topology.Comment: 21 pages with 2 figures, SU-4240-579 (figures corrected in this version

Is the propensity to emit alarm calls associated with health status?

This work was supported by the National Geographic Society, UCLA (Faculty Senate and the Division of Life Sciences), a RMBL research fellowship, and by the National Science Foundation (NSF) (IDBR-0754247, and DEB-1119660 and 1557130 to D.T.B., as well as DBI-0242960, 0731346, and 1226713 to the RMBL).Peer reviewedPublisher PD

Hot dense capsule implosion cores produced by z-pinch dynamic hohlraum radiation

Hot dense capsule implosions driven by z-pinch x-rays have been measured for the first time. A ~220 eV dynamic hohlraum imploded 1.7-2.1 mm diameter gas-filled CH capsules which absorbed up to ~20 kJ of x-rays. Argon tracer atom spectra were used to measure the Te~ 1keV electron temperature and the ne ~ 1-4 x10^23 cm-3 electron density. Spectra from multiple directions provide core symmetry estimates. Computer simulations agree well with the peak compression values of Te, ne, and symmetry, indicating reasonable understanding of the hohlraum and implosion physics.Comment: submitted to Phys. Rev. Let

Preferential sites for intramolecular glucosepane cross-link formation in type I collagen: A thermodynamic study

The extracellular matrix (ECM) undergoes progressive age-related stiffening and loss of proteolytic digestibility due to an increase in concentration of advanced glycation end products (AGEs). The most abundant AGE, glucosepane, accumulates in collagen with concentrations over 100 times greater than all other AGEs. Detrimental collagen stiffening properties are believed to play a significant role in several age-related diseases such as osteoporosis and cardiovascular disease. Currently little is known of the potential location of covalently cross-linked glucosepane formation within collagen molecules; neither are there reports on how the respective cross-link sites affect the physical and biochemical properties of collagen. Using fully atomistic molecular dynamics simulations (MD) we have identified six sites where the formation of a covalent intra-molecular glucosepane cross-link within a single collagen molecule in a fibrillar environment is energetically favourable. Identification of these favourable sites enables us to align collagen cross-linking with experimentally observed changes to the ECM. For example, formation of glucosepane was found to be energetically favourable within close proximity of the Matrix Metalloproteinase-1 (MMP1) binding site, which could potentially disrupt collagen degradation.fals

The Core of the Participatory Budgeting Problem

In participatory budgeting, communities collectively decide on the allocation of public tax dollars for local public projects. In this work, we consider the question of fairly aggregating the preferences of community members to determine an allocation of funds to projects. This problem is different from standard fair resource allocation because of public goods: The allocated goods benefit all users simultaneously. Fairness is crucial in participatory decision making, since generating equitable outcomes is an important goal of these processes. We argue that the classic game theoretic notion of core captures fairness in the setting. To compute the core, we first develop a novel characterization of a public goods market equilibrium called the Lindahl equilibrium, which is always a core solution. We then provide the first (to our knowledge) polynomial time algorithm for computing such an equilibrium for a broad set of utility functions; our algorithm also generalizes (in a non-trivial way) the well-known concept of proportional fairness. We use our theoretical insights to perform experiments on real participatory budgeting voting data. We empirically show that the core can be efficiently computed for utility functions that naturally model our practical setting, and examine the relation of the core with the familiar welfare objective. Finally, we address concerns of incentives and mechanism design by developing a randomized approximately dominant-strategy truthful mechanism building on the exponential mechanism from differential privacy

Changing nurses' views of the therapeutic environment: randomised controlled trial

BACKGROUND: Although patients value evidence-based therapeutic activities, little is known about nurses' perceptions.AimsTo investigate whether implementing an activities training programme would positively alter staff perceptions of the ward or be detrimental through the increased workload (trial registration: ISRCTN 06545047). METHOD: We conducted a stepped wedge cluster randomised trial involving 16 wards with psychology-led nurse training as the intervention. The main outcome was a staff self-report measure of perceptions of the ward (VOTE) and secondary outcomes measuring potential deterioration were the Index of Work Satisfaction (IWS) and the Maslach Burnout Inventory (MBI). Data were analysed using mixed-effects regression models, with repeated assessments from staff over time. RESULTS: There were 1075 valid outcome measurements from 539 nursing staff. VOTE scores did not change over time (standardised effect size 0.04, 95% CI -0.09 to 0.18, P = 0.54), neither did IWS or MBI scores (IWS, standardised effect size 0.02, 95% CI -0.11 to 0.16, P = 0.74; MBI standardised effect size -0.09, 95% CI -0.24 to 0.06, P = 0.24). There was a mean increase of 1.5 activities per ward (95% CI -0.4 to 3.4, P = 0.12) and on average 6.3 more patients attended groups (95% CI -4.1 to 16.6, P = 0.23) following training. Staff feedback on training was positive. CONCLUSIONS: Our training programme did not change nurses' perceptions of the ward, job satisfaction or burnout. During the study period many service changes occurred, most having a negative impact through increased pressure on staffing, patient mix and management so it is perhaps unsurprising that we found no benefits or reduction in staff skill.Declaration of interestNone

Dilemma and Quantum Battle of Sexes

We analysed quantum version of the game battle of sexes using a general initial quantum state. For a particular choice of initial entangled quantum state it is shown that the classical dilemma of the battle of sexes can be resolved and a unique solution of the game can be obtained.Comment: Revised, Latex, 9 pages, no figure, corresponding author's email: [email protected]