Distributed Testing of Excluded Subgraphs

We study property testing in the context of distributed computing, under the classical CONGEST model. It is known that testing whether a graph is triangle-free can be done in a constant number of rounds, where the constant depends on how far the input graph is from being triangle-free. We show that, for every connected 4-node graph H, testing whether a graph is H-free can be done in a constant number of rounds too. The constant also depends on how far the input graph is from being H-free, and the dependence is identical to the one in the case of testing triangles. Hence, in particular, testing whether a graph is K_4-free, and testing whether a graph is C_4-free can be done in a constant number of rounds (where K_k denotes the k-node clique, and C_k denotes the k-node cycle). On the other hand, we show that testing K_k-freeness and C_k-freeness for k>4 appear to be much harder. Specifically, we investigate two natural types of generic algorithms for testing H-freeness, called DFS tester and BFS tester. The latter captures the previously known algorithm to test the presence of triangles, while the former captures our generic algorithm to test the presence of a 4-node graph pattern H. We prove that both DFS and BFS testers fail to test K_k-freeness and C_k-freeness in a constant number of rounds for k>4

Is Large Lepton Mixing Excluded?

The original \bnum -(or $\bar{\nu}_{\tau}$-) energy spectrum from the gravitational collapse of a star has a larger average energy than the spectrum for \bnue since the opacity of \bnue exeeds that of \bnum (or $\nu_{\tau}$). Flavor neutrino conversion, \bnue $\leftrightarrow$ \bnum, induced by lepton mixing results in partial permutation of the original \bnue and \bnum spectra. An upper bound on the permutation factor, $p \leq 0.35$ (99$\%$ CL) is derived using the data from SN1987A and the different models of the neutrino burst. The relation between the permutation factor and the vacuum mixing angle is established, which leads to the upper bound on this angle. The excluded region, $\sin^2 2\theta > 0.7 - 0.9$, covers the regions of large mixing angle solutions of the solar neutrino problem: ``just-so" and, partly, MSW, as well as part of region of $\nu_{e} - \nu_{\mu}$ oscillation space which could be responsible for the atmospheric muon neutrino deficit. These limits are sensitive to the predicted neutrino spectrum and can be strengthened as supernova models improve.Comment: 20 pages, TeX file. For hardcopy with figures contact [email protected]. Institute for Advanced Study number AST 93/1

Queueing process with excluded-volume effect

We introduce an extension of the M/M/1 queueing process with a spatial structure and excluded- volume effect. The rule of particle hopping is the same as for the totally asymmetric simple exclusion process (TASEP). A stationary-state solution is constructed in a slightly arranged matrix product form of the open TASEP. We obtain the critical line that separates the parameter space depending on whether the model has the stationary state. We calculate the average length of the model and the number of particles and show the monotonicity of the probability of the length in the stationary state. We also consider a generalization of the model with backward hopping of particles allowed and an alternate joined system of the M/M/1 queueing process and the open TASEP.Comment: 9 figure

Is natural higgsino-only dark matter excluded?

The requirement of electroweak naturalness in supersymmetric (SUSY) models of particle physics necessitates light higgsinos not too far from the weak scale characterized by m(weak)~ m(W,Z,h)~100 GeV. On the other hand, LHC Higgs mass measurements and sparticle mass limits point to a SUSY breaking scale in the multi-TeV regime. Under such conditions, the lightest SUSY particle is expected to be a mainly higgsino-like neutralino with non-negligible gaugino components (required by naturalness). The computed thermal WIMP abundance in natural SUSY models is then found to be typically a factor 5-20 below its measured value. To gain concordance with observations, either an additional DM particle (the axion is a well-motivated possibility) must be present or additional non-thermal mechanisms must augment the neutralino abundance. We compare present direct and indirect WIMP detection limits to three natural SUSY models based on gravity-, anomaly- and mirage-mediation. We show that the case of natural higgsino-only dark matter where non-thermal production mechanisms augment its relic density, is essentially excluded by a combination of direct detection constraints from PandaX-II, LUX and Xenon-1t experiments, and by bounds from Fermi-LAT/MAGIC observations of gamma rays from dwarf spheroidal galaxies.Comment: 16 pages with 6 .png figures; some added references for version