Proof Complexity of Systems of (Non-Deterministic) Decision Trees and Branching Programs

This paper studies propositional proof systems in which lines are sequents of decision trees or branching programs, deterministic or non-deterministic. Decision trees (DTs) are represented by a natural term syntax, inducing the system LDT, and non-determinism is modelled by including disjunction, ?, as primitive (system LNDT). Branching programs generalise DTs to dag-like structures and are duly handled by extension variables in our setting, as is common in proof complexity (systems eLDT and eLNDT). Deterministic and non-deterministic branching programs are natural nonuniform analogues of log-space (L) and nondeterministic log-space (NL), respectively. Thus eLDT and eLNDT serve as natural systems of reasoning corresponding to L and NL, respectively. The main results of the paper are simulation and non-simulation results for tree-like and dag-like proofs in LDT, LNDT, eLDT and eLNDT. We also compare them with Frege systems, constant-depth Frege systems and extended Frege systems

Polylogarithmic Approximation for Generalized Minimum Manhattan Networks

Given a set of $n$ terminals, which are points in $d$-dimensional Euclidean space, the minimum Manhattan network problem (MMN) asks for a minimum-length rectilinear network that connects each pair of terminals by a Manhattan path, that is, a path consisting of axis-parallel segments whose total length equals the pair's Manhattan distance. Even for $d=2$, the problem is NP-hard, but constant-factor approximations are known. For $d \ge 3$, the problem is APX-hard; it is known to admit, for any \eps > 0, an O(n^\eps)-approximation. In the generalized minimum Manhattan network problem (GMMN), we are given a set $R$ of $n$ terminal pairs, and the goal is to find a minimum-length rectilinear network such that each pair in $R$ is connected by a Manhattan path. GMMN is a generalization of both MMN and the well-known rectilinear Steiner arborescence problem (RSA). So far, only special cases of GMMN have been considered. We present an $O(\log^{d+1} n)$-approximation algorithm for GMMN (and, hence, MMN) in $d \ge 2$ dimensions and an $O(\log n)$-approximation algorithm for 2D. We show that an existing $O(\log n)$-approximation algorithm for RSA in 2D generalizes easily to $d>2$ dimensions.Comment: 14 pages, 5 figures; added appendix and figure

Near Real-Time Optimal Prediction of Adverse Events in Aviation Data

The prediction of anomalies or adverse events is a challenging task, and there are a variety of methods which can be used to address the problem. In this paper, we demonstrate how to recast the anomaly prediction problem into a form whose solution is accessible as a level-crossing prediction problem. The level-crossing prediction problem has an elegant, optimal, yet untested solution under certain technical constraints, and only when the appropriate modeling assumptions are made. As such, we will thoroughly investigate the resilience of these modeling assumptions, and show how they affect final performance. Finally, the predictive capability of this method will be assessed by quantitative means, using both validation and test data containing anomalies or adverse events from real aviation data sets that have previously been identified as operationally significant by domain experts. It will be shown that the formulation proposed yields a lower false alarm rate on average than competing methods based on similarly advanced concepts, and a higher correct detection rate than a standard method based upon exceedances that is commonly used for prediction

Translating knowledge into practice: content analysis of online resources about sexual difficulties for individuals with traumatic brain injury

For many individuals with traumatic brain injury (TBI), the Internet is the only available source of information regarding their sexual problems following TBI. This study aimed to evaluate the content and the quality of patient or carer information that is readily available on the Internet about specific aspects of sexuality after TBI. A purposive (non-exhaustive) sample of eight leaflets available on the Internet related to sexuality following TBI was analysed using content analysis. Decreased desire was reported as the main sexual difficulty following TBI (87.5%), followed by inappropriate sexual behaviour (62.5%). Among the strategies to overcome these difficulties, all leaflets recommended seeking help from healthcare professionals; 42.8% were centred on the carer or the family, and only 28.5% was directly addressed to the individual with TBI. The information available overemphasises disinhibition, underscores other aspects of sexuality (e.g. sexual risk and inability to fantasise), and is conceived mainly for carers and families. A bias assuming that most individuals with TBI are involved in a romantic relationship was also present. Adolescents, women, older people, single people, and non-heterosexual individuals were not adequately represented. There is a need for Internet resources to provide specific recommendations for these groups

Ageing, telomeres, senescence, and liver injury

Populations in developed countries continue to grow older and an understanding of the ageing process to allow healthy ageing carries important medical implications. Older individuals are more susceptible to most acquired liver disorders and more vulnerable to the consequences of liver disease. Accordingly, age is a critical determinant of outcome for hepatitis C virus infection and liver transplantation. In this review we describe changes in the ageing liver and discuss mechanisms of senescence at the cellular level. In particular, we focus on mechanisms by which inflammation, oxidative stress, and oncogenic stress accelerate cellular senescence. In the setting of chronic hepatic injury and inflammation, cellular senescence functions as an essential stress-response mechanism to limit the proliferation of damaged cells and reduce the risk of malignancy, but this benefit is achieved at the expense of senescence-related organ dysfunction. The dual role of cell senescence in chronic liver disease will make this an intriguing but challenging area for future clinical interventions

Bond-orientational ordering and shear rigidity in modulated colloidal liquids

From Landau-Alexander-McTague theory and Monte-Carlo simulation results we show that the modulated liquid obtained by subjecting a colloidal system to a periodic laser modulation has long range bond-orientational order and non-zero shear rigidity. From infinite field simulation results we show that in the modulated liquid phase, the translational order parameter correlation function decays to zero exponentially while the correlation function for the bond-orientational order saturates to a finite value at large distances.Comment: 8 pages, elsart documentclass, to be published in Physica A as part of proceedings for Stat-Phys 3, Calcutt