The group testing problem consists of determining a small set of defective items from a larger set of items based on a number of possibly-noisy tests, and is relevant in applications such as medical testing, communication protocols, pattern matching, and many more. One of the defining features of the group testing problem is the distinction between the non-adaptive and adaptive settings: In the...

We study the problem of generalized uniformity testing [BC17] of a discrete probability distribution: Given samples from a probability distribution p over an unknown discrete domain Ω, we want to distinguish, with probability at least 2/3, between the case that p is uniform on some subset of Ω versus -far, in total variation distance, from any such uniform distribution. We establish tight bound...

Recent advances in noiseless non-adaptive group testing have led to a precise asymptotic characterization of the number tests required for high-probability recovery sublinear regime $k = n^{\theta }$ (with notation="LaTeX">$\theta \in (0,1)$ ), with notation="LaTeX">$n$ individuals among which n...

Given oracle access to some boolean function f, how many queries do we need to test whether f is linear? Or monotone? Or whether its output is completely determined by a small number of the input variables? This thesis studies these and related questions in the framework of property testing introduced by Rubinfeld and Sudan (’96). The results of this thesis are grouped into three main lines of ...

symmetric division deg index is one of the 148 discrete adriatic indices that showed good predictive properties on the testing sets provided by international academy of mathematical chemistry.symmetric division deg index is defined by$$sdd(g) = sume left( frac{min{d_u,d_v}}{max{d_u,d_v}} + frac{max{d_u,d_v}}{min{d_u,d_v}} right),$$where $d_i$ is the degree of vertex $i$ in graph $g$.in this pap...

t his study investigates the factors affecting the demand for new residential buildings in urban areas of iran during 1976-2010. the demand function for new residential buildings in urban areas was estimated and then the existence of a long-run relationship among variables of this function was studied using the bounds testing of the autoregressive distributed lag co-integration procedure. the t...

this paper investigates the relationship between macroeconomic instability and private investment of the iranian economy. the study uses a trivariate var(2)-garch(1,1)-in-mean with diagonal bekk approach to proxied inflation and exchange rate uncertainties as the main indicators of macroeconomic instability. moreover, bounds testing approach to level relationship applied to investigate the long...

We present a new methodology for proving distribution testing lower bounds, establishing a connection between distribution testing and the simultaneous message passing (SMP) communication model. Extending the framework of Blais, Brody, and Matulef [15], we show a simple way to reduce (private-coin) SMP problems to distribution testing problems. This method allows us to prove new distribution te...