Shortly before beginning his questioning of the slave-boy, Socrates reports an opinion which he considers to be “Something true, it seems to me, and beautiful”. The reported opinion concludes “For inquiry and learning as a whole is recollection”. To illustrate the conclusion, Plato has Socrates enter into a detailed mathematical discussion. Nowhere else does Plato present mathematics in any det...

The online square detection problem is to detect the first occurrence of a square in a string whose characters are provided as input one at a time. Recall that a square is a string that is a concatenation of two identical strings. In this paper we present an algorithm solving this problem in O(n log σ) time and linear space on ordered alphabet, where σ is the number of different letters in the ...

An efficient and computationally linear algorithm is derived for total least squares solution of adaptive filtering problem, when both input and output signals are contaminated by noise. The proposed total least mean squares (TLMS) algorithm is designed by recursively computing an optimal solution of adaptive TLS problem by minimizing instantaneous value of weighted cost function. Convergence a...

Square is a multivariate quadratic encryption scheme proposed in 2009. It is a specialization of Hidden Field Equations by using only odd characteristic elds and also X as its central map. In addition, it uses embedding to reduce the number of variables in the public key. However, the system was broken at Asiacrypt 2009 using a di erential attack. At PQCrypto 2010 Clough and Ding proposed two n...

Dans une permutation, un record est maximum ou minimum, en partant de la droite gauche. Les éléments d’une permutation peuvent être classés deux types : les records (dits points extérieurs) et autres intérieurs). permutations sans point intérieur ont été étudiées sous le nom carrées. Ici, nous explorons ayant nombre fini intérieurs, dites quasi-carrées. Contrairement aux carrées, l’énumération ...

the paper presents unified analytical solution for combining high-frequency and low-frequency economic time-series by additive and proportional denton methods with parametrical dependence on the initial values of variable and indicator in evident form. this solution spans denton’s original and cholette’s advanced benchmarking initial conditions as the subcases. computational complexity of the o...

This paper presents a planar biochip consisting of electromagnetically coupled, symmetric, square open loops for the multiparameter microwave characterization of deionized water, a phosphate-buffered saline solution, and a fructose-deionized water solution. The characterization additionally includes the probing of an ultralow glucose concentration in a very small volume of human sera and in sol...