Estimating graph parameters with random walks

An algorithm observes the trajectories of random walks over an unknown graph $G$, starting from the same vertex $x$, as well as the degrees along the trajectories. For all finite connected graphs, one can estimate the number of edges $m$ up to a bounded factor in $O\left(t_{\mathrm{rel}}^{3/4}\sqrt{m/d}\right)$ steps, where $t_{\mathrm{rel}}$ is the relaxation time of the lazy random walk on $G$ and $d$ is the minimum degree in $G$. Alternatively, $m$ can be estimated in $O\left(t_{\mathrm{unif}} +t_{\mathrm{rel}}^{5/6}\sqrt{n}\right)$, where $n$ is the number of vertices and $t_{\mathrm{unif}}$ is the uniform mixing time on $G$. The number of vertices $n$ can then be estimated up to a bounded factor in an additional $O\left(t_{\mathrm{unif}}\frac{m}{n}\right)$ steps. Our algorithms are based on counting the number of intersections of random walk paths $X,Y$, i.e. the number of pairs $(t,s)$ such that $X_t=Y_s$. This improves on previous estimates which only consider collisions (i.e., times $t$ with $X_t=Y_t$). We also show that the complexity of our algorithms is optimal, even when restricting to graphs with a prescribed relaxation time. Finally, we show that, given either $m$ or the mixing time of $G$, we can compute the "other parameter" with a self-stopping algorithm

Subexponential Size Hitting Sets for Bounded Depth Multilinear Formulas

In this paper we give subexponential size hitting sets for bounded depth multilinear arithmetic formulas. Using the known relation between black-box PIT and lower bounds we obtain lower bounds for these models. For depth-3 multilinear formulas, of size exp(n^delta), we give a hitting set of size exp(~O(n^(2/3 + 2*delta/3))). This implies a lower bound of exp(~Omega(n^(1/2))) for depth-3 multilinear formulas, for some explicit polynomial. For depth-4 multilinear formulas, of size exp(n^delta), we give a hitting set of size exp(~O(n^(2/3 + 4*delta/3)). This implies a lower bound of exp(~Omega(n^(1/4))) for depth-4 multilinear formulas, for some explicit polynomial. A regular formula consists of alternating layers of +,* gates, where all gates at layer i have the same fan-in. We give a hitting set of size (roughly) exp(n^(1-delta)), for regular depth-d multilinear formulas of size exp(n^delta), where delta = O(1/sqrt(5)^d)). This result implies a lower bound of roughly exp(~Omega(n^(1/sqrt(5)^d))) for such formulas. We note that better lower bounds are known for these models, but also that none of these bounds was achieved via construction of a hitting set. Moreover, no lower bound that implies such PIT results, even in the white-box model, is currently known. Our results are combinatorial in nature and rely on reducing the underlying formula, first to a depth-4 formula, and then to a read-once algebraic branching program (from depth-3 formulas we go straight to read-once algebraic branching programs)

Police-citizen relations in São Paulo: fear and legitimacy

In São Paulo, Brazil, many people fear crime. Some also fear the police, but can also tolerate extreme police violence. One of the keys to legitimate police power is procedural justice because it enhances legitimacy, normatively appropriate police behaviour and encourages people to self-regulate, as Jonathan Jackson (LSE & University of Sydney Law School), Thiago Oliveira (Oxford University) and Ben Bradford (UCL) found

Quasi-Stationary Distributions for Models of Heterogeneous Catalysis

We construct the quasi-stationary (QS) distribution for two models of heterogeneous catalysis having two absorbing states: the ZGB model for the oxidation of CO, and a version with noninstantaneous reactions. Using a mean-field-like approximation, we study the quasi-stationary surface coverages, moment ratios and the lifetime of the QS state. We also derive an improved, consistent one-site mean-field theory for the ZGB model.Comment: 18 pages, 13 figure

Are trustworthiness and legitimacy “hard to win, easy to lose”? A longitudinal test of the asymmetry thesis of police-citizen contact

Objectives Test the asymmetry thesis of police-citizen contact that police trustworthiness and legitimacy are affected more by negative than by positive experiences of interactions with legal agents by analyzing changes in attitudes towards the police after an encounter with the police. Test whether prior attitudes moderate the impact of contact on changes in attitudes towards the police. Methods A two-wave panel survey of a nationally representative sample of Australian adults measured people’s beliefs about police trustworthiness (procedural fairness and effectiveness), their duty to obey the police, their contact with the police between the two waves, and their evaluation of those encounters in terms of process and outcome. Analysis is carried out using autoregressive structural equation modeling and latent moderated structural models. Results The association between both process and outcome evaluation of police-citizen encounters and changes in attitudes towards the police is asymmetrical for trust in police effectiveness, symmetrical for trust in procedural fairness, and asymmetrical (in the opposite direction expected) for duty to obey the police. Little evidence of heterogeneity in the association between encounters and trust in procedural fairness and duty to obey, but prior levels of perceived effectiveness moderate the association between outcome evaluation and changes in trust in police effectiveness. Conclusions The association between police-citizen encounters and attitudes towards the police may not be as asymmetrical as previously thought, particularly for changes in trust in procedural fairness and legitimacy. Policy implications include considering public-police interactions as ‘teachable moments’ and potential sources for enhancing police trustworthiness and legitimacy

Influence of methylene fluorination and chain length on the hydration shell structure and thermodynamics of linear diols

The interplay between the local hydration shell structure, the length of hydrophobic solutes, and their identity (perfluorinated or not) remains poorly understood. We address this issue by combining Raman–multivariate curve resolution (Raman-MCR) spectroscopy, simulation, and quantum-mechanical calculations to quantify the thermodynamics and the first principle interactions behind the formation of defects in the hydration shell of alkyl–diol and perfluoroalkyl–diol chains. The hydration shell of the fluorinated diols contains substantially more defects than that of the nonfluorinated diols; these defects are water hydroxy groups that do not donate hydrogen bonds and which either point to the solute (radial-dangling OH) or not (nonradial-dangling OH). The number of radial-dangling OH defects per carbon decreases for longer chains and toward the interior of the fluorinated diols, mainly due to less favorable electrostatics and exchange interactions; nonradial-dangling OH defects per carbon increase with chain length. In contrast, the hydration shell of the nonfluorinated diols only contains radial-dangling defects, which become more abundant toward the center of the chain and for larger chains, predominantly because of more favorable dispersion interactions. These results have implications for how the folding of macromolecules, ligand binding to biomacromolecules, and chemical reactions at water–oil interfaces could be modified through the introduction of fluorinated groups or solvents

Rapid determination of some of the most used pesticides in Northeast Portugal as emerging contaminants in rivers by SPME/GC-MS

In this communication the development of an analytical methodology is presented for the monitoring of five emerging pollutants, namely, alachlor, metolachlor, heptachlor, dimethoate, and terbuthylazine. These compounds are among the most used pesticides in the northeast region of Portugal and Tunisia. The complete experimental methodology is optimized based on the simultaneous extraction and concentration of all five pesticides from aqueous matrices, by means of solid-phase micro-extraction (SPME) followed by detection and quantification using gas chromatography with mass spectrometry (GC-MS). The optimization of the extraction step is performed using a polydimethylsiloxane-divinylbenzene (PDMS-DVB) coated SPME fiber by direct immersion (DI-SPME) in the aqueous sample.info:eu-repo/semantics/publishedVersio

The impact of the uncertainties in the 12C(α, γ ) 16O reaction rate on the evolution of low- to intermediate-mass stars

One of the largest uncertainties in stellar evolutionary computations is the accuracy of the considered reaction rates. The 12C(α, γ ) 16O reaction is particularly important for the study of low- and intermediate-mass stars as it determines the final C/O ratio in the core which influences the white dwarf (WD) cooling evolution. Thus, there is a need for a study of how the computations of WDs and their progenitors that are made to date may be affected by the uncertainties of the 12C(α, γ ) 16O reaction rates. In this work, we compute fully evolutionary sequences using the MESA code with initial masses in the range of 0.90 ≤ Mi/M ≤ 3.05. We consider different adopted reaction rates, obtained from the literature, as well as the extreme limits within their uncertainties. As expected, we find that previous to the core helium burning (CHB) stage, there are no changes to the evolution of the stars. However, the subsequent stages are all affected by the uncertainties of the considered reaction rate. In particular, we find differences to the convective core mass during the CHB stage which may affect pulsation properties of subdwarfs, the number of thermal pulses during the asymptotic giant branch and trends between final oxygen abundance in the core and the progenitor masses of the remnant WDs

Systemic treatment of advanced and metastatic urothelial cancer: The landscape in Australia

The 5-year survival rate of metastatic urothelial carcinoma (mUC) is estimated to be as low as 5%. Currently, systemic platinum-based chemotherapy followed by avelumab maintenance therapy is the only first-line treatment for mUC that has an overall survival benefit. Cisplatin-based chemotherapy (usually in combination with gemcitabine) is the preferred treatment but carboplatin is substituted where contraindications to cisplatin exist. Treatment with immune checkpoint inhibitors, antibody-drug conjugates, and kinase inhibitors has not yet demonstrated superiority to chemotherapy as first-line therapy and remains investigational in this setting. A recent media release indicates that chemotherapy plus nivolumab gives an OS advantage as first-line treatment but results of this study have not yet been made public. Pembrolizumab remains an option in those having primary progression on first-line chemotherapy or within 12 months of neoadjuvant chemotherapy. The antibody-drug conjugate, enfortumab vedotin has TGA approval for patients whose cancer has progressed following chemotherapy and immunotherapy and has just received a positive Pharmaceutical Benefits Scheme recommendation. The use of molecular screens for somatic genetic mutations, gene amplifications, and protein expression is expanding as drugs that target such abnormalities show promise. However, despite these advances, a substantial proportion of patients with mUC have significant barriers to receiving any treatment, including advancing age, frailty, and comorbidities, and less toxic, effective therapies are needed