The evolution of the cover time

The cover time of a graph is a celebrated example of a parameter that is easy to approximate using a randomized algorithm, but for which no constant factor deterministic polynomial time approximation is known. A breakthrough due to Kahn, Kim, Lovasz and Vu yielded a (log log n)^2 polynomial time approximation. We refine this upper bound, and show that the resulting bound is sharp and explicitly computable in random graphs. Cooper and Frieze showed that the cover time of the largest component of the Erdos-Renyi random graph G(n,c/n) in the supercritical regime with c>1 fixed, is asymptotic to f(c) n \log^2 n, where f(c) tends to 1 as c tends to 1. However, our new bound implies that the cover time for the critical Erdos-Renyi random graph G(n,1/n) has order n, and shows how the cover time evolves from the critical window to the supercritical phase. Our general estimate also yields the order of the cover time for a variety of other concrete graphs, including critical percolation clusters on the Hamming hypercube {0,1}^n, on high-girth expanders, and on tori Z_n^d for fixed large d. For the graphs we consider, our results show that the blanket time, introduced by Winkler and Zuckerman, is within a constant factor of the cover time. Finally, we prove that for any connected graph, adding an edge can increase the cover time by at most a factor of 4.Comment: 14 pages, to appear in CP

The Bristol model:An abyss called a Cohen real

We construct a model M of ZF which lies between L and L[c] for a Cohen real c and does not have the form L(x) for any set x. This is loosely based on the unwritten work done in a Bristol workshop about Woodin's HOD Conjecture in 2011. The construction given here allows for a finer analysis of the needed assumptions on the ground models, thus taking us one step closer to understanding models of ZF, and the HOD Conjecture and its relatives. This model also provides a positive answer to a question of Grigorieff about intermediate models of ZF, and we use it to show the failure of Kinna-Wagner Principles in ZF

Distinct immune signatures in directly treated and distant tumors result from TLR adjuvants and focal ablation.

Both adjuvants and focal ablation can alter the local innate immune system and trigger a highly effective systemic response. Our goal is to determine the impact of these treatments on directly treated and distant disease and the mechanisms for the enhanced response obtained by combinatorial treatments. Methods: We combined RNA-sequencing, flow cytometry and TCR-sequencing to dissect the impact of immunotherapy and of immunotherapy combined with ablation on local and systemic immune components. Results: With administration of a toll-like receptor agonist agonist (CpG) alone or CpG combined with same-site ablation, we found dramatic differences between the local and distant tumor environments, where the directly treated tumors were skewed to high expression of F4/80, Cd11b and Tnf and the distant tumors to enhanced Cd11c, Cd3 and Ifng. When ablation was added to immunotherapy, 100% (n=20/20) of directly treated tumors and 90% (n=18/20) of distant tumors were responsive. Comparing the combined ablation-immunotherapy treatment to immunotherapy alone, we find three major mechanistic differences. First, while ablation alone enhanced intratumoral antigen cross-presentation (up to ~8% of CD45+ cells), systemic cross-presentation of tumor antigen remained low. Combining same-site ablation with CpG amplified cross-presentation in the draining lymph node (~16% of CD45+ cells) compared to the ablation-only (~0.1% of CD45+ cells) and immunotherapy-only cohorts (~10% of CD45+ cells). Macrophages and DCs process and present this antigen to CD8+ T-cells, increasing the number of unique T-cell receptor rearrangements in distant tumors. Second, type I interferon (IFN) release from tumor cells increased with the ablation-immunotherapy treatment as compared with ablation or immunotherapy alone. Type I IFN release is synergistic with toll-like receptor activation in enhancing cytokine and chemokine expression. Expression of genes associated with T-cell activation and stimulation (Eomes, Prf1 and Icos) was 27, 56 and 89-fold higher with ablation-immunotherapy treatment as compared to the no-treatment controls (and 12, 32 and 60-fold higher for immunotherapy-only treatment as compared to the no-treatment controls). Third, we found that the ablation-immunotherapy treatment polarized macrophages and dendritic cells towards a CD169 subset systemically, where CD169+ macrophages are an IFN-enhanced subpopulation associated with dead-cell antigen presentation. Conclusion: While the local and distant responses are distinct, CpG combined with ablative focal therapy drives a highly effective systemic immune response

Monoamines, BDNF, Dehydroepiandrosterone, DHEA-Sulfate, and Childhood Depression—An Animal Model Study

Basal levels of monoamines and DHEA in four main limbic brain regions were measured in prepubertal Wistar Kyoto (WKY) rats (a putative animal model of childhood depression). Basal levels of “Brain-Derived Neurotrophic Factor (BDNF)” were also determined in two regions in the hippocampus, compared with Wistar strain controls. In the second phase, we examined the responsiveness of prepubertal WKY rats to different types of chronic antidepressant treatments: Fluoxetine, Desipramine, and dehydroepiandrosterone sulfate (DHEAS). WKY prepubertal rats exhibited different monoamine levels in the limbic system, reduced DHEA levels in the VTA and lower levels of BDNF in the hippocampus CA3 region compared to controls. In prepubertal WKY rats, only treatment with DHEAS produced a statistically significant decrease in immobility, compared to saline-administered controls in the forced swim test. Wistar controls were not affected by any antidepressant. The results imply that DHEA(S) and BDNF may be involved in the pathophysiology and pharmacotherapy of childhood depression

The Alexander-Orbach conjecture holds in high dimensions

We examine the incipient infinite cluster (IIC) of critical percolation in regimes where mean-field behavior has been established, namely when the dimension d is large enough or when d>6 and the lattice is sufficiently spread out. We find that random walk on the IIC exhibits anomalous diffusion with the spectral dimension d_s=4/3, that is, p_t(x,x)= t^{-2/3+o(1)}. This establishes a conjecture of Alexander and Orbach. En route we calculate the one-arm exponent with respect to the intrinsic distance.Comment: 25 pages, 2 figures. To appear in Inventiones Mathematica

Phase Space Approach to Solving the Time-independent Schr\"odinger Equation

We propose a method for solving the time independent Schr\"odinger equation based on the von Neumann (vN) lattice of phase space Gaussians. By incorporating periodic boundary conditions into the vN lattice [F. Dimler et al., New J. Phys. 11, 105052 (2009)] we solve a longstanding problem of convergence of the vN method. This opens the door to tailoring quantum calculations to the underlying classical phase space structure while retaining the accuracy of the Fourier grid basis. The method has the potential to provide enormous numerical savings as the dimensionality increases. In the classical limit the method reaches the remarkable efficiency of 1 basis function per 1 eigenstate. We illustrate the method for a challenging two-dimensional potential where the FGH method breaks down.Comment: 5 figures. Includes supplementary material. arXiv admin note: substantial text overlap with arXiv:1010.258

Comparative expression profiling and sequence characterization of ATP1A1 gene associated with heat tolerance in tropically adapted cattle

Climate change is an imminent threat to livestock production. One adaptation strategy is selection for heat tolerance. While it is established that the ATP1A1 gene and its product play an important role in the response to many stressors, there has been no attempt to characterize the sequence or to perform expression profiling of the gene in production animals. We undertook a field experiment to compare the expression profiles of ATP1A1 in heat-tolerant Vechur and Kasaragod cattle (Bos taurus indicus) with the profile of a heat-susceptible crossbreed (B. t. taurus × B. t. indicus). The cattle were exposed to heat stress while on pasture in the hot summer season. The environmental stress was quantified using the temperature humidity index (THI), while the heat tolerance of each breed was assessed using a heat tolerance coefficient (HTC). The ATP1A1 mRNA of Vechur cattle was amplified from cDNA and sequenced. The HTC varied significantly between the breeds and with time-of-day (p < 0.01). The breed–time-of-day interaction was also significant (p < 0.01). The relative expression of ATP1A1 differed between heat-tolerant and heat-susceptible breeds (p = 0.02). The expression of ATP1A1 at 08:00, 10:00 and 12:00, and the breed–time-of-day interaction, were not significant. The nucleotide sequence of Vechur ATP1A1 showed 99% homology with the B. t. taurus sequence. The protein sequence showed 98% homology with B. t. taurus cattle and with B. grunniens (yak) and 97.7% homology with Ovis aries (sheep). A molecular clock analysis revealed evidence of divergent adaptive evolution of the ATP1A1 gene favoring climate resilience in Vechur cattle. These findings further our knowledge of the relationship between the ATP1A1 gene and heat tolerance in phenotypically incongruent animals. We propose that ATP1A1 could be used in marker assisted selection (MAS) for heat tolerance