Myers conjectured that for every integer s there exists a positive constant C such that for all integers t every graph of average degree at least Ct contains a Ks,t minor. We prove the following stronger result: for every 0 < ε < 10−16 there exists a number t0 = t0(ε) such that for all integers t ≥ t0 and s ≤ εt/ log t every graph of average degree at least (1 + ε)t contains a Ks,t minor. The b...

We revisit the construction of high noise, almost optimal rate list decodable code of Guruswami [1]. Guruswami showed that if one can explicitly construct optimal extractors then one can build an explicit (1− 2, O( 1 2 )) list decodable codes of rate Ω( 2 log 1 2 ) and alphabet size 2 1 2 ·log 1 2 . We show that if one replaces the expander component in the construction with an unbalanced dispe...

Low coherence interference microscopy (LCIM) provides high spatial phase sensitivity, i.e., speckle free and coherent noise quantitative images of the test specimens. Due to low temporal (TC) length light source, LCIM requires precise adjustment optical path difference (OPD) between object reference arm, which is only a few micrometers. Consequently, previously demonstrated systems are implemen...

Entropy regularized optimal transport and its multi-marginal generalization have attracted increasing attention in various applications, particular due to efficient Sinkhorn-like algorithms for computing plans. However, it is often desirable that the marginals of plan do not match given measures exactly, which led introduction so-called unbalanced transport. Since methods were examined setting ...

We document that even though the normal distribution is a good approximation to the nature of aggregate fluctuations, it severely underpredicts the frequency of large economic downturns. We then provide a model that can explain these facts simultaneously. Our model shows that the propagation of microeconomic shocks through input-output linkages can fundamentally reshape the distribution of aggr...