On the Computational Complexity of Vertex Integrity and Component Order Connectivity

The Weighted Vertex Integrity (wVI) problem takes as input an $n$-vertex graph $G$, a weight function $w:V(G)\to\mathbb{N}$, and an integer $p$. The task is to decide if there exists a set $X\subseteq V(G)$ such that the weight of $X$ plus the weight of a heaviest component of $G-X$ is at most $p$. Among other results, we prove that: (1) wVI is NP-complete on co-comparability graphs, even if each vertex has weight $1$; (2) wVI can be solved in $O(p^{p+1}n)$ time; (3) wVI admits a kernel with at most $p^3$ vertices. Result (1) refutes a conjecture by Ray and Deogun and answers an open question by Ray et al. It also complements a result by Kratsch et al., stating that the unweighted version of the problem can be solved in polynomial time on co-comparability graphs of bounded dimension, provided that an intersection model of the input graph is given as part of the input. An instance of the Weighted Component Order Connectivity (wCOC) problem consists of an $n$-vertex graph $G$, a weight function $w:V(G)\to \mathbb{N}$, and two integers $k$ and $l$, and the task is to decide if there exists a set $X\subseteq V(G)$ such that the weight of $X$ is at most $k$ and the weight of a heaviest component of $G-X$ is at most $l$. In some sense, the wCOC problem can be seen as a refined version of the wVI problem. We prove, among other results, that: (4) wCOC can be solved in $O(\min\{k,l\}\cdot n^3)$ time on interval graphs, while the unweighted version can be solved in $O(n^2)$ time on this graph class; (5) wCOC is W[1]-hard on split graphs when parameterized by $k$ or by $l$; (6) wCOC can be solved in $2^{O(k\log l)} n$ time; (7) wCOC admits a kernel with at most $kl(k+l)+k$ vertices. We also show that result (6) is essentially tight by proving that wCOC cannot be solved in $2^{o(k \log l)}n^{O(1)}$ time, unless the ETH fails.Comment: A preliminary version of this paper already appeared in the conference proceedings of ISAAC 201

Full Database Reconstruction with Access and Search Pattern Leakage

The widespread use of cloud computing has enabled several database providers to store their data on servers in the cloud and answer queries from those servers. In order to protect the confidentiality of data in the cloud, a database can be stored in encrypted form and all queries can be executed on the encrypted database. Recent research results suggest that a curious cloud provider may be able to decrypt some of the items in the database after seeing a large number of queries and their (encrypted) results. In this paper, we focus on one-dimensional databases that support range queries and develop an attack that can achieve full database reconstruction, inferring the exact value of every element in the database. We consider an encrypted database whose records have values from a given universe of $N$ consecutive integers.Our attack assumes access pattern and search pattern leakage. It succeeds after the attacker has seen each of the possible query results at least once, independent of their distribution. If we assume that the client issues queries uniformly at random, we can decrypt the entire database with high probability after observing $O(N^2 \log N)$ queries

The impact of multiple sclerosis on the identity of mothers in Italy

Purpose: This paper reports on one of the themes that emerged from the analysis of the study, regarding the perceived influence of multiple sclerosis (MS) on the identity of mothers in the socio-cultural context of Italy. Method: In-depth interviews were conducted with 16 women at various stages of MS, with follow up interviews with seven of the women. Phenomenology guided the methodology and the analysis was conducted using interpretative phenomenological analysis. Results: Through the research the value of motherhood to the women who participated emerged. The findings illustrated how many strove to maintain controlof their MS, which led to some making comparisons of themselves and other mothers and feeling different. Some women described how they adjusted their roles and found strength in being mothers but others spoke of their feelings of loss. Most women described living in the moment, appreciating the present and living each day as it came. Another significant experience was fear of stigma, both realized in the form of “pity” from others, and the perceived and actual associated stigma for their families. This contributed to why some women were reluctant to disclose their condition. The mothers who took part in this study differed in how they perceived their disabled identity. Conclusion: Although this study was conducted in the socio-cultural setting of Italy, the findings have implications for professionals working with disabled mothers and women with MS in Italy and beyond; including recognizing the value associated with fully identifying oneself as a mother, rather than solely focusing on doingmothering tasks. • Implications for Rehabilitation • Professionals need to be mindful of the value of motherhood for women with multiple sclerosis. • Professionals should support women who feel like they are battling with maintaining control of their multiple sclerosis, who may be adjusting their identity as mothers; recognizing that they may be influenced by the stage of their multiple sclerosis and whether they were diagnosed before or after having their children. • Women can have feelings of loss related to their ability to fully participate in their children’s lives and professionals should work with women to help them identify the value of their mothering role not only in physically participating in activities but also in being emotionally and physically present as a mother

On the Uniform Random Generation of Non Deterministic Automata Up to Isomorphism

In this paper we address the problem of the uniform random generation of non deterministic automata (NFA) up to isomorphism. First, we show how to use a Monte-Carlo approach to uniformly sample a NFA. Secondly, we show how to use the Metropolis-Hastings Algorithm to uniformly generate NFAs up to isomorphism. Using labeling techniques, we show that in practice it is possible to move into the modified Markov Chain efficiently, allowing the random generation of NFAs up to isomorphism with dozens of states. This general approach is also applied to several interesting subclasses of NFAs (up to isomorphism), such as NFAs having a unique initial states and a bounded output degree. Finally, we prove that for these interesting subclasses of NFAs, moving into the Metropolis Markov chain can be done in polynomial time. Promising experimental results constitute a practical contribution.Comment: Frank Drewes. CIAA 2015, Aug 2015, Umea, Sweden. Springer, 9223, pp.12, 2015, Implementation and Application of Automata - 20th International Conferenc

The climatic importance of uncertainties in regional aerosol-cloud radiative forcings over recent decades

This is the final version of the article. Available from American Meteorological Society via the DOI in this record.Regional patterns of aerosol radiative forcing are important for understanding climate change on decadal time scales. Uncertainty in aerosol forcing is likely to vary regionally and seasonally because of the short aerosol lifetime and heterogeneous emissions. Here the sensitivity of regional aerosol cloud albedo effect (CAE) forcing to 31 aerosol process parameters and emission fluxes is quantified between 1978 and 2008. The effects of parametric uncertainties on calculations of the balance of incoming and outgoing radiation are found to be spatially and temporally dependent. Regional uncertainty contributions of opposite sign cancel in global-mean forcing calculations, masking the regional importance of some parameters. Parameters that contribute little to uncertainty in Earth's global energy balance during recent decades make significant contributions to regional forcing variance. Aerosol forcing sensitivities are quantified within 11 climatically important regions, where surface temperatures are thought to influence large-scale climate effects. Substantial simulated uncertainty in CAE forcing in the eastern Pacific leaves open the possibility that apparent shifts in the mean ENSO state may result from a forced aerosol signal on multidecadal time scales. A likely negative aerosol CAE forcing in the tropical North Atlantic calls into question the relationship between Northern Hemisphere aerosol emission reductions and CAE forcing of sea surface temperatures in the main Atlantic hurricane development region on decadal time scales. Simulated CAE forcing uncertainty is large in the North Pacific, suggesting that the role of the CAE in altering Pacific tropical storm frequency and intensity is also highly uncertain.Data can be made available upon request from the corresponding author. L. A. Regayre is funded by a Doctoral Training Grant from the Natural Environment Research Council (NERC) and a CASE studentship with the Met Office Hadley Centre. B. B. B. Booth was supported by the Joint UK DECC/Defra Met Office Hadley Centre Climate Programme (GA01101). K. S. Carslaw acknowledges funding from the Royal Society Wolfson Award. We acknowledge funding from NERC under AEROS and GASSP Grants NE/G006172/1 and NE/J024252/1. This work made use of the facilities of N8 HPC provided and funded by the N8 consortium and EPSRC (EP/K000225/1). The Met Office Hadley Centre is coordinated by the University of Leeds and the University of Manchester. The authors thank three anonymous reviewers for their constructive comments on this article

Deformation of Codimension-2 Surface and Horizon Thermodynamics

The deformation equation of a spacelike submanifold with an arbitrary codimension is given by a general construction without using local frames. In the case of codimension-1, this equation reduces to the evolution equation of the extrinsic curvature of a spacelike hypersurface. In the more interesting case of codimension-2, after selecting a local null frame, this deformation equation reduces to the well known (cross) focusing equations. We show how the thermodynamics of trapping horizons is related to these deformation equations in two different formalisms: with and without introducing quasilocal energy. In the formalism with the quasilocal energy, the Hawking mass in four dimension is generalized to higher dimension, and it is found that the deformation of this energy inside a marginal surface can be also decomposed into the contributions from matter fields and gravitational radiation as in the four dimension. In the formalism without the quasilocal energy, we generalize the definition of slowly evolving future outer trapping horizons proposed by Booth to past trapping horizons. The dynamics of the trapping horizons in FLRW universe is given as an example. Especially, the slowly evolving past trapping horizon in the FLRW universe has close relation to the scenario of slow-roll inflation. Up to the second order of the slowly evolving parameter in this generalization, the temperature (surface gravity) associated with the slowly evolving trapping horizon in the FLRW universe is essentially the same as the one defined by using the quasilocal energy.Comment: Latex, 61 pages, no figures; v2, type errors corrected; v3, references and comments are added, English is improved, to appear in JHE

Local Optical Probe of Motion and Stress in a multilayer graphene NEMS

Nanoelectromechanical systems (NEMSs) are emerging nanoscale elements at the crossroads between mechanics, optics and electronics, with significant potential for actuation and sensing applications. The reduction of dimensions compared to their micronic counterparts brings new effects including sensitivity to very low mass, resonant frequencies in the radiofrequency range, mechanical non-linearities and observation of quantum mechanical effects. An important issue of NEMS is the understanding of fundamental physical properties conditioning dissipation mechanisms, known to limit mechanical quality factors and to induce aging due to material degradation. There is a need for detection methods tailored for these systems which allow probing motion and stress at the nanometer scale. Here, we show a non-invasive local optical probe for the quantitative measurement of motion and stress within a multilayer graphene NEMS provided by a combination of Fizeau interferences, Raman spectroscopy and electrostatically actuated mirror. Interferometry provides a calibrated measurement of the motion, resulting from an actuation ranging from a quasi-static load up to the mechanical resonance while Raman spectroscopy allows a purely spectral detection of mechanical resonance at the nanoscale. Such spectroscopic detection reveals the coupling between a strained nano-resonator and the energy of an inelastically scattered photon, and thus offers a new approach for optomechanics

The Climatic Importance of Uncertainties in Regional Aerosol-Cloud Radiative Forcings over Recent Decades

Regional patterns of aerosol radiative forcing are important for understanding climate change on decadal time scales. Uncertainty in aerosol forcing is likely to vary regionally and seasonally because of the short aerosol lifetime and heterogeneous emissions. Here the sensitivity of regional aerosol cloud albedo effect (CAE) forcing to 31 aerosol process parameters and emission fluxes is quantified between 1978 and 2008. The effects of parametric uncertainties on calculations of the balance of incoming and outgoing radiation are found to be spatially and temporally dependent. Regional uncertainty contributions of opposite sign cancel in global-mean forcing calculations, masking the regional importance of some parameters. Parameters that contribute little to uncertainty in Earth’s global energy balance during recent decades make significant contributions to regional forcing variance. Aerosol forcing sensitivities are quantified within 11 climatically important regions, where surface temperatures are thought to influence large-scale climate effects. Substantial simulated uncertainty in CAE forcing in the eastern Pacific leaves open the possibility that apparent shifts in the mean ENSO state may result from a forced aerosol signal on multidecadal time scales. A likely negative aerosol CAE forcing in the tropical North Atlantic calls into question the relationship between Northern Hemisphere aerosol emission reductions and CAE forcing of sea surface temperatures in the main Atlantic hurricane development region on decadal time scales. Simulated CAE forcing uncertainty is large in the North Pacific, suggesting that the role of the CAE in altering Pacific tropical storm frequency and intensity is also highly uncertain

Induced Disjoint Paths in Circular-Arc Graphs in Linear Time

The Induced Disjoint Paths problem is to test whether a graph G with k distinct pairs of vertices (si,ti) contains paths P1,…,Pk such that Pi connects si and ti for i=1,…,k, and Pi and Pj have neither common vertices nor adjacent vertices (except perhaps their ends) for 1≤