On Approximating the Number of kk-cliques in Sublinear Time

We study the problem of approximating the number of $k$-cliques in a graph when given query access to the graph. We consider the standard query model for general graphs via (1) degree queries, (2) neighbor queries and (3) pair queries. Let $n$ denote the number of vertices in the graph, $m$ the number of edges, and $C_k$ the number of $k$-cliques. We design an algorithm that outputs a $(1+\varepsilon)$-approximation (with high probability) for $C_k$, whose expected query complexity and running time are O\left(\frac{n}{C_k^{1/k}}+\frac{m^{k/2}}{C_k}\right)\poly(\log n,1/\varepsilon,k). Hence, the complexity of the algorithm is sublinear in the size of the graph for $C_k = \omega(m^{k/2-1})$. Furthermore, we prove a lower bound showing that the query complexity of our algorithm is essentially optimal (up to the dependence on $\log n$, $1/\varepsilon$ and $k$). The previous results in this vein are by Feige (SICOMP 06) and by Goldreich and Ron (RSA 08) for edge counting ($k=2$) and by Eden et al. (FOCS 2015) for triangle counting ($k=3$). Our result matches the complexities of these results. The previous result by Eden et al. hinges on a certain amortization technique that works only for triangle counting, and does not generalize for larger cliques. We obtain a general algorithm that works for any $k\geq 3$ by designing a procedure that samples each $k$-clique incident to a given set $S$ of vertices with approximately equal probability. The primary difficulty is in finding cliques incident to purely high-degree vertices, since random sampling within neighbors has a low success probability. This is achieved by an algorithm that samples uniform random high degree vertices and a careful tradeoff between estimating cliques incident purely to high-degree vertices and those that include a low-degree vertex

An Inverse Compton Scattering Origin of X-ray Flares from Sgr A*

The X-ray and near-IR emission from Sgr A* is dominated by flaring, while a quiescent component dominates the emission at radio and sub-mm wavelengths. The spectral energy distribution of the quiescent emission from Sgr A* peaks at sub-mm wavelengths and is modeled as synchrotron radiation from a thermal population of electrons in the accretion flow, with electron temperatures ranging up to $\sim 5-20$\,MeV. Here we investigate the mechanism by which X-ray flare emission is produced through the interaction of the quiescent and flaring components of Sgr A*. The X-ray flare emission has been interpreted as inverse Compton, self-synchrotron-Compton, or synchrotron emission. We present results of simultaneous X-ray and near-IR observations and show evidence that X-ray peak flare emission lags behind near-IR flare emission with a time delay ranging from a few to tens of minutes. Our Inverse Compton scattering modeling places constraints on the electron density and temperature distributions of the accretion flow and on the locations where flares are produced. In the context of this model, the strong X-ray counterparts to near-IR flares arising from the inner disk should show no significant time delay, whereas near-IR flares in the outer disk should show a broadened and delayed X-ray flare.Comment: 22 pages, 6 figures, 2 tables, AJ (in press

Helping or Hurting?: Understanding Women’s Perceptions of Male Allies

In the past decade, organizational scholars have begun to explore the role of allies in mitigating workplace discrimination toward women and members of minority groups. However, this nascent literature has, to this point, failed to consider the perspective of targets of ally behavior. That is, we do not yet know how targets of discrimination experience others’ intervention or advocacy. To begin to understand these issues, we examine target perceptions of allyship through a qualitative critical incident approach, asking women to describe experiences in which a man has effectively and ineffectively acted as an ally to them in the workplace. Our findings from surveying 100 women provide new insights regarding who engages in ally behaviors, what behaviors these allies enact, when and where the behaviors take place, and why participants believed their male ally engaged in this behavior

Simulation of transient energy distributions in sub-ns streamer formation

Breakdown and streamer formation is simulated in atmospheric pressure nitrogen for a 2D planar electrode system. A PIC code with multigrid potential solver is used to simulate the evolution of the non-equilibrium ionization front on sub-nanosecond timescales. The ion and electron energy distributions are computed, accounting for the inclusion of inelastic scattering of electrons, and collisionally excited metastable production and ionization. Of particular interest is the increased production of metastable and low-energy ions and electrons when the applied field is reversed during the progress of the ionization front, giving insight into the improved species yields in nanosecond pulsed systems

A Cellular Automaton Model for Diffusive and Dissipative Systems

We study a cellular automaton model, which allows diffusion of energy (or equivalently any other physical quantities such as mass of a particular compound) at every lattice site after each timestep. Unit amount of energy is randomly added onto a site. Whenever the local energy content of a site reaches a fixed threshold $E_{c1}$, energy will be dissipated. Dissipation of energy propagates to the neighboring sites provided that the energy contents of those sites are greater than or equal to another fixed threshold $E_{c2} (\leq E_{c1})$. Under such dynamics, the system evolves into three different types of states depending on the values of $E_{c1}$ and $E_{c2}$ as reflected in their dissipation size distributions, namely: localized peaks, power laws, or exponential laws. This model is able to describe the behaviors of various physical systems including the statistics of burst sizes and burst rates in type-I X-ray bursters. Comparisons between our model and the famous forest-fire model (FFM) are made.Comment: in REVTEX 3.0. Figures available on request. Extensively revised. Accepted by Phys.Rev.

Continuity of the four-point function of massive ϕ44\phi_4^4-theory above threshold

In this paper we prove that the four-point function of massive \vp_4^4-theory is continuous as a function of its independent external momenta when posing the renormalization condition for the (physical) mass on-shell. The proof is based on integral representations derived inductively from the perturbative flow equations of the renormalization group. It closes a longstanding loophole in rigorous renormalization theory in so far as it shows the feasibility of a physical definition of the renormalized coupling.Comment: 23 pages; to appear in Rev. Math. Physics few corrections, two explanatory paragraphs adde

Meta-transcriptomic discovery of a divergent circovirus and a chaphamaparvovirus in captive reptiles with proliferative respiratory syndrome

Viral pathogens are being increasingly described in association with mass morbidity and mortality events in reptiles. However, our knowledge of reptile viruses remains limited. Herein, we describe the meta-transcriptomic investigation of a mass morbidity and mortality event in a colony of central bearded dragons (Pogona vitticeps) in 2014. Severe, extensive proliferation of the respiratory epithelium was consistently found in affected dragons. Similar proliferative lung lesions were identified in bearded dragons from the same colony in 2020 in association with increased intermittent mortality. Total RNA sequencing identified two divergent DNA viruses: a reptile-infecting circovirus, denoted bearded dragon circovirus (BDCV), and the first exogeneous reptilian chaphamaparvovirus—bearded dragon chaphamaparvovirus (BDchPV). Phylogenetic analysis revealed that BDCV was most closely related to bat-associated circoviruses, exhibiting 70% amino acid sequence identity in the Replicase (Rep) protein. In contrast, in the nonstructural (NS) protein, the newly discovered BDchPV showed approximately 31%–35% identity to parvoviruses obtained from tilapia fish and crocodiles in China. Subsequent specific PCR assays revealed BDCV and BDchPV in both diseased and apparently normal captive reptiles, although only BDCV was found in those animals with proliferative pulmonary lesions and respiratory disease. This study expands our understanding of viral diversity in captive reptiles