In this paper, the efficacy of seven data classification methods; Decision Tree (DT), k-Nearest Neighbor (k-NN), Logistic Regression (LogR), Naïve Bayes (NB), C4.5, Support Vector Machine (SVM) and Linear Classifier (LC) with regard to the Area Under Curve (AUC) metric have been compared. The effects of parameters including size of the dataset, kind of the independent attributes, and the number...

Let D(n, r) be a random r-out regular directed multigraph on the set of vertices {1, . . . , n}. In this work, we establish that for every r ≥ 2, there exists ηr > 0 such that diam(D(n, r)) = (1 + ηr + o(1)) logr n. Our techniques also allow us to bound some extremal quantities related to the stationary distribution of a simple random walk on D(n, r). In particular, we determine the asymptotic ...

Abstract: We establish a conjecture of Brizolis that for every prime p > 3 there is a primitive root r and an integer t in the interval [1, p− 1] with logr t = t. Here, logr is the discrete logarithm function to the base r for the cyclic group (Z/pZ)×. Tools include a numerically explicit version of the Pólya–Vinogradov inequality for the sum of values of a Dirichlet character on an interval, s...

In this paper, we prove an almost-optimal hardness for Max k-CSPR based on Khot’s Unique Games Conjecture (UGC). In Max k-CSPR, we are given a set of predicates each of which depends on exactly k variables. Each variable can take any value from 1, 2, . . . , R. The goal is to find an assignment to variables that maximizes the number of satisfied predicates. Assuming the Unique Games Conjecture,...

Reservoir Computing (RC) is a relatively recent architecture for using recurrent neural networks. It has shown interesting performance in a wide range of tasks despite the simple training rules. We use it here in a logistic regression (LogR) framework. Considering non-Markovian time series with a hidden variable, we show that RC can be used to estimate the transition probabilities at each time ...

A binary code with covering radius R is a subset C of the hypercube Qn = {0, 1}n such that every x ∈ Qn is within Hamming distance R of some codeword c ∈ C, where R is as small as possible. For a fixed coordinate i ∈ [n], define C b , for b ∈ {0, 1}, to be the set of codewords with a b in the ith position. Then C is normal if there exists an i ∈ [n] such that for any v ∈ Qn, the sum of the Hamm...

The total organic carbon content (TOC) is a crucial indicator for the evaluation of shale gas reservoirs, traditionally estimated by measuring cores, cuttings or sidewall cores in laboratory with source rock evaluation instruments. Limited by the number of rock samples, the experimental results are not continuous and it is impossible to show the whole face of a source rock bed. Continuous high ...

Using our interferometric angular diameter measurements of seven classical Cepheids reported in Kervella et al. (2003, Paper I), complemented by previously existing measurements, we derive new calibrations of the Cepheids Period–Radius (P–R) and Period–Luminosity (P–L) relations. We obtain a P–R relation of logR = [0.767 ± 0.009] logP + [1.091 ± 0.011], only 1σ away from the relation obtained b...

Let H denote the discrete Heisenberg group, equipped with a word metric dW associated to some finite symmetric generating set. We show that if (X, ‖ ·‖) is a p-convex Banach space then for any Lipschitz function f : H→ X there exist x, y ∈ H with dW (x, y) arbitrarily large and ‖f(x)− f(y)‖ dW (x, y) . ( log log dW (x, y) log dW (x, y) )1/p . (1) We also show that any embedding into X of a ball...