Sequential Posted Price Mechanisms with Correlated Valuations

We study the revenue performance of sequential posted price mechanisms and some natural extensions, for a general setting where the valuations of the buyers are drawn from a correlated distribution. Sequential posted price mechanisms are conceptually simple mechanisms that work by proposing a take-it-or-leave-it offer to each buyer. We apply sequential posted price mechanisms to single-parameter multi-unit settings in which each buyer demands only one item and the mechanism can assign the service to at most k of the buyers. For standard sequential posted price mechanisms, we prove that with the valuation distribution having finite support, no sequential posted price mechanism can extract a constant fraction of the optimal expected revenue, even with unlimited supply. We extend this result to the the case of a continuous valuation distribution when various standard assumptions hold simultaneously. In fact, it turns out that the best fraction of the optimal revenue that is extractable by a sequential posted price mechanism is proportional to ratio of the highest and lowest possible valuation. We prove that for two simple generalizations of these mechanisms, a better revenue performance can be achieved: if the sequential posted price mechanism has for each buyer the option of either proposing an offer or asking the buyer for its valuation, then a Omega(1/max{1,d}) fraction of the optimal revenue can be extracted, where d denotes the degree of dependence of the valuations, ranging from complete independence (d=0) to arbitrary dependence (d=n-1). Moreover, when we generalize the sequential posted price mechanisms further, such that the mechanism has the ability to make a take-it-or-leave-it offer to the i-th buyer that depends on the valuations of all buyers except i's, we prove that a constant fraction (2-sqrt{e})/4~0.088 of the optimal revenue can be always be extracted.Comment: 29 pages, To appear in WINE 201

Primary Care Atrial Fibrillation Service: outcomes from consultant-led anticoagulation assessment clinics in the primary care setting in the UK

OBJECTIVE: Stroke-risk in atrial fibrillation (AF) can be significantly reduced by appropriate thromboembolic prophylaxis. However, National Institute for Health and Care Excellence estimates suggest that up to half of eligible patients with AF are not anticoagulated, with severe consequences for stroke prevention. We aimed to determine the outcome of an innovative Primary Care AF (PCAF) service on anticoagulation uptake in a cohort of high-risk patients with AF in the UK. METHODS: The PCAF service is a novel cooperative pathway providing specialist resources within general practitioner (GP) practices. It utilises a four-phase protocol to identify high-risk patients with AF (CHA(2)DS(2)-VASc ≥1) who are suboptimally anticoagulated, and delivers Consultant-led anticoagulation assessment within the local GP practice. We assessed rates of anticoagulation in high-risk patients before and after PCAF service intervention, and determined compliance with newly-initiated anticoagulation at follow-up. RESULTS: The PCAF service was delivered in 56 GP practices (population 386 624; AF prevalence 2.1%) between June 2012 and June 2014. 1579 high-risk patients with AF with suboptimal anticoagulation (either not taking any anticoagulation or taking warfarin but with a low time-in-therapeutic-range) were invited for review, with 86% attending. Of 1063 eligible patients on no anticoagulation, 1020 (96%) agreed to start warfarin (459 (43%)) or a non-vitamin K antagonist oral anticoagulant (NOAC, 561 (53%)). The overall proportion of eligible patients receiving anticoagulation improved from 77% to 95% (p<0.0001). Additionally, 111/121 (92%) patients suboptimally treated with warfarin agreed to switch to a NOAC. Audit of eight practices after 195 (185–606) days showed that 90% of patients started on a new anticoagulant therapy had continued treatment. Based on data extrapolated from previous studies, around 30–35 strokes per year may have been prevented in these previously under-treated high-risk patients. CONCLUSIONS: Systematic identification of patients with AF with high stroke-risk and consultation in PCAF consultant-led clinics effectively delivers oral anticoagulation to high-risk patients with AF in the community

Sex differences in the influence of body mass index on anatomical architecture of brain networks.

Background/objectivesThe brain has a central role in regulating ingestive behavior in obesity. Analogous to addiction behaviors, an imbalance in the processing of rewarding and salient stimuli results in maladaptive eating behaviors that override homeostatic needs. We performed network analysis based on graph theory to examine the association between body mass index (BMI) and network measures of integrity, information flow and global communication (centrality) in reward, salience and sensorimotor regions and to identify sex-related differences in these parameters.Subjects/methodsStructural and diffusion tensor imaging were obtained in a sample of 124 individuals (61 males and 63 females). Graph theory was applied to calculate anatomical network properties (centrality) for regions of the reward, salience and sensorimotor networks. General linear models with linear contrasts were performed to test for BMI and sex-related differences in measures of centrality, while controlling for age.ResultsIn both males and females, individuals with high BMI (obese and overweight) had greater anatomical centrality (greater connectivity) of reward (putamen) and salience (anterior insula) network regions. Sex differences were observed both in individuals with normal and elevated BMI. In individuals with high BMI, females compared to males showed greater centrality in reward (amygdala, hippocampus and nucleus accumbens) and salience (anterior mid-cingulate cortex) regions, while males compared to females had greater centrality in reward (putamen) and sensorimotor (posterior insula) regions.ConclusionsIn individuals with increased BMI, reward, salience and sensorimotor network regions are susceptible to topological restructuring in a sex-related manner. These findings highlight the influence of these regions on integrative processing of food-related stimuli and increased ingestive behavior in obesity, or in the influence of hedonic ingestion on brain topological restructuring. The observed sex differences emphasize the importance of considering sex differences in obesity pathophysiology

Characterisation of ATP-dependent Mur ligases involved in the biogenesis of cell wall peptidoglycan in Mycobacterium tuberculosis.

ATP-dependent Mur ligases (Mur synthetases) play essential roles in the biosynthesis of cell wall peptidoglycan (PG) as they catalyze the ligation of key amino acid residues to the stem peptide at the expense of ATP hydrolysis, thus representing potential targets for antibacterial drug discovery. In this study we characterized the division/cell wall (dcw) operon and identified a promoter driving the co-transcription of mur synthetases along with key cell division genes such as ftsQ and ftsW. Furthermore, we have extended our previous investigations of MurE to MurC, MurD and MurF synthetases from Mycobacterium tuberculosis. Functional analyses of the pure recombinant enzymes revealed that the presence of divalent cations is an absolute requirement for their activities. We also observed that higher concentrations of ATP and UDP-sugar substrates were inhibitory for the activities of all Mur synthetases suggesting stringent control of the cytoplasmic steps of the peptidoglycan biosynthetic pathway. In line with the previous findings on the regulation of mycobacterial MurD and corynebacterial MurC synthetases via phosphorylation, we found that all of the Mur synthetases interacted with the Ser/Thr protein kinases, PknA and PknB. In addition, we critically analyzed the interaction network of all of the Mur synthetases with proteins involved in cell division and cell wall PG biosynthesis to re-evaluate the importance of these key enzymes as novel therapeutic targets in anti-tubercular drug discovery

Analysis of symmetries in models of multi-strain infections

In mathematical studies of the dynamics of multi-strain diseases caused by antigenically diverse pathogens, there is a substantial interest in analytical insights. Using the example of a generic model of multi-strain diseases with cross-immunity between strains, we show that a significant understanding of the stability of steady states and possible dynamical behaviours can be achieved when the symmetry of interactions between strains is taken into account. Techniques of equivariant bifurcation theory allow one to identify the type of possible symmetry-breaking Hopf bifurcation, as well as to classify different periodic solutions in terms of their spatial and temporal symmetries. The approach is also illustrated on other models of multi-strain diseases, where the same methodology provides a systematic understanding of bifurcation scenarios and periodic behaviours. The results of the analysis are quite generic, and have wider implications for understanding the dynamics of a large class of models of multi-strain diseases

Dynamics of fully coupled rotators with unimodal and bimodal frequency distribution

We analyze the synchronization transition of a globally coupled network of N phase oscillators with inertia (rotators) whose natural frequencies are unimodally or bimodally distributed. In the unimodal case, the system exhibits a discontinuous hysteretic transition from an incoherent to a partially synchronized (PS) state. For sufficiently large inertia, the system reveals the coexistence of a PS state and of a standing wave (SW) solution. In the bimodal case, the hysteretic synchronization transition involves several states. Namely, the system becomes coherent passing through traveling waves (TWs), SWs and finally arriving to a PS regime. The transition to the PS state from the SW occurs always at the same coupling, independently of the system size, while its value increases linearly with the inertia. On the other hand the critical coupling required to observe TWs and SWs increases with N suggesting that in the thermodynamic limit the transition from incoherence to PS will occur without any intermediate states. Finally a linear stability analysis reveals that the system is hysteretic not only at the level of macroscopic indicators, but also microscopically as verified by measuring the maximal Lyapunov exponent.Comment: 22 pages, 11 figures, contribution for the book: Control of Self-Organizing Nonlinear Systems, Springer Series in Energetics, eds E. Schoell, S.H.L. Klapp, P. Hoeve

Visibility Representations of Boxes in 2.5 Dimensions

We initiate the study of 2.5D box visibility representations (2.5D-BR) where vertices are mapped to 3D boxes having the bottom face in the plane $z=0$ and edges are unobstructed lines of sight parallel to the $x$- or $y$-axis. We prove that: $(i)$ Every complete bipartite graph admits a 2.5D-BR; $(ii)$ The complete graph $K_n$ admits a 2.5D-BR if and only if $n \leq 19$; $(iii)$ Every graph with pathwidth at most $7$ admits a 2.5D-BR, which can be computed in linear time. We then turn our attention to 2.5D grid box representations (2.5D-GBR) which are 2.5D-BRs such that the bottom face of every box is a unit square at integer coordinates. We show that an $n$-vertex graph that admits a 2.5D-GBR has at most $4n - 6 \sqrt{n}$ edges and this bound is tight. Finally, we prove that deciding whether a given graph $G$ admits a 2.5D-GBR with a given footprint is NP-complete. The footprint of a 2.5D-BR $\Gamma$ is the set of bottom faces of the boxes in $\Gamma$.Comment: Appears in the Proceedings of the 24th International Symposium on Graph Drawing and Network Visualization (GD 2016

Diffuse White Matter Signal Abnormalities on Magnetic Resonance Imaging Are Associated With Human Immunodeficiency Virus Type 1 Viral Escape in the Central Nervous System Among Patients With Neurological Symptoms

Background: Human immunodeficiency virus type 1 (HIV-1) can replicate independently in extravascular compartments such as the central nervous system, resulting in either cerebrospinal fluid (CSF) discordance (viral load [VL] in CSF 0.5 log10 copies HIV-1 RNA greater than plasma VL) or escape (detection of HIV VL >50 copies/mL in CSF in patients with suppressed plasma VL <50 copies/mL). Both discordance and escape may be associated with neurological symptoms. We explored risk factors for CSF discordance and escape in patients presenting with diverse neurological problems. Methods: HIV-infected adult patients undergoing diagnostic lumbar puncture (LP) at a single center between 2011 and 2015 were included in the analysis. Clinical and neuroimaging variables associated with CSF discordance/escape were identified using multivariate logistic regression. Results: One hundred forty-six patients with a median age of 45.3 (interquartile range [IQR], 39.6–51.5) years underwent 163 LPs. Median CD4 count was 430 (IQR, 190–620) cells/µL. Twenty-four (14.7%) LPs in 22 patients showed CSF discordance, of which 10 (6.1%) LPs in 9 patients represented CSF escape. In multivariate analysis, both CSF discordance and escape were associated with diffuse white matter signal abnormalities (DWMSAs) on cranial magnetic resonance imaging (adjusted odds ratio, 10.3 [95% confidence interval {CI}, 2.3–45.0], P = .007 and 56.9 [95% CI, 4.0–882.8], P = .01, respectively). All 7 patients with CSF escape (10 LPs) had been diagnosed with HIV >7 years prior to LP, and 6 of 6 patients with resistance data had documented evidence of drug-resistant virus in plasma. Conclusions: Among patients presenting with diverse neurological problems, CSF discordance or escape was observed in 15%, with treatment-experienced patients dominating the escape group. DWMSAs in HIV-infected individuals presenting with neurological problems should raise suspicion of possible CSF discordance/escape

Cardy and Kerr

The Kerr/CFT correspondence employs the Cardy formula to compute the entropy of the left moving CFT states. This computation, which correctly reproduces the Bekenstein--Hawking entropy of the four-dimensional extremal Kerr black hole, is performed in a regime where the temperature is of order unity rather than in a high-temperature regime. We show that the comparison of the entropy of the extreme Kerr black hole and the entropy in the CFT can be understood within the Cardy regime by considering a D0-D6 system with the same entropic properties.Comment: 20 pages; LaTeX; JHEP format; v.2 references added, v.3 Section 4 adde