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A set R⊂N is called rational if it is well approximable by finite unions of arithmetic progressions, meaning that for every \unicode[STIX]x1D716>0 there exists a set B=⋃i=1raiN+bi, where $a_{1},\ldots ,a_ ...
A subfamily {F-1, F-2, ..., F-vertical bar P vertical bar} subset of F is a copy of the poset P if there exists a bijection i : P -> {F-1, F-2, ..., F-vertical bar P vertical bar}, such that p
A language is said to be homogeneous when all its words have the same length. Homogeneous languages thus form a monoid under concatenation. It becomes freely commutative under the simultaneous actions of every permutation group G(n) on the collection of ho ...
We review the notion of a linearity-generating (LG) process introduced by Gabaix and relate LG processes to linear-rational (LR) models studied by Filipović et al. We show that every LR model can be represented as an LG process and vice versa. We find that ...
Given a graph H and a set of graphs F, let ex(n, H, F) denote the maximum possible number of copies of H in an T-free graph on n vertices. We investigate the function ex(n, H, F), when H and members of F are cycles. Let C-k denote the cycle of length k and ...
Modular robots (MRs) consist of similar modules that can be configured into different shapes. MRs introduce a number of benefits over conventional robots specifically designed for a task. Self-reconfigurable modular robots (SRMRs) are a sub-category of MRs ...
This paper presents two new approaches for finding the homogenized coefficients of multiscale elliptic PDEs. Standard approaches for computing the homogenized coefficients suffer from the so-called resonance error, originating from a mismatch between the t ...
While optimization is well studied for real-valued functions f:RN→R, many physical problems are (partially) specified in terms of complex-valued functions fc:CN→CM. Current optimization packag ...
How can we explain consciousness? This question has become a vibrant topic of neuroscience research in recent decades. A large body of empirical results has been accumulated, and many theories have been proposed. Certain theories suggest that consciousness ...
The history of giant viruses began in 2003 with the identification of Acanthamoeba polyphaga mimivirus. Since then, giant viruses of amoeba enlightened an unknown part of the viral world, and every discovery and characterization of a new giant virus modifi ...
