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In this paper, the construction of finite-length binary sequences whose nonlinear complexity is not less than half of the length is investigated. By characterizing the structure of the sequences, an algorithm is proposed to generate all…
As suggested by Currie, we apply the probabilistic method to problems regarding pattern avoidance. Using techniques from analytic combinatorics, we calculate asymptotic pattern occurrence statistics and use them in conjunction with the…
The purpose of the present paper is to show few examples of nonlinear PDEs (mostly with strong geometric features) for which there is a hidden convex structure. This is not only a matter of curiosity. Once the convex structure is…
Some methods aim to correct or test for relationships or to reconstruct the pedigree, or family tree. We show that these methods cannot resolve ties for correct relationships due to identifiability of the pedigree likelihood which is the…
Mathematical inequalities, combined with atomic-physics sum rules, enable one to derive lower and upper bounds for the Rosseland and/or Planck mean opacities. The resulting constraints must be satisfied, either for pure elements or…
In this work we consider morphisms that preserve well-known non-repeating properties: squarefreeness, cubefreeness, overlap-freeness and weak squarefreeness. Up to the present moment only the morphisms preserving three out of four…
We present some results, both rigorously mathematical and computational, showing unexpected relations between different identities expressing nilpotence in nonassociative algebras, and formulate a number of conjectural generalizations and…
We formulate N-fold supersymmetry in quantum mechanical systems with reflection operators. As in the cases of other systems, they possess the two significant characters of N-fold supersymmetry, namely, almost isospectrality and weak…
We investigate four properties related to an elliptic curve $E_t$ in Legendre form with parameter $t$: the curve $E_{t}$ has complex multiplication, $E_{-t}$ has complex multiplication, a point on $E_t$ with abscissa $2$ is of finite order,…
Hidden variables are extra components added to try to banish counterintuitive features of quantum mechanics. We start with a quantum-mechanical model and describe various properties that can be asked of a hidden-variable model. We present…
Binomial ideals are special polynomial ideals with many algorithmically and theoretically nice properties. We discuss the problem of deciding if a given polynomial ideal is binomial. While the methods are general, our main motivation and…
According to Born's rule quantum probabilities are given by the overlap between the system state and measurement states in a quite symmetrical way. This means that both contribute to any observed nonclassical effect that is usually…
Accidental symmetries in effective field theories can be established by computing and comparing Hilbert series. This invites us to study them with the tools of invariant theory. Applying this technology, we spotlight three classes of…
Nonclassical properties of correlations-- like unpredictability, no-cloning and uncertainty-- are known to follow from two assumptions: nonlocality and no-signaling. For two-input-two-output correlations, we derive these properties from a…
We show the existence of regular combinatorial objects which previously were not known to exist. Specifically, for a wide range of the underlying parameters, we show the existence of non-trivial orthogonal arrays, t-designs, and t-wise…
This paper presents a systematic study of the structure of non-solvable cyclic metric Lie algebras. A cyclic metric is a symmetric bilinear form satisfying a cyclic cocycle condition, which arises naturally in the contexts of…
We show that many bounded rationality patterns of choice can be alternatively represented as testable models of limited consideration, and we elicit the features of the associated unobserved consideration sets from the observed choice.…
We present two practical and widely applicable methods, including some criteria and a general procedure, for detecting Brunnian property of a link, if each component is known to be unknot. The methods are based on observation and handwork.…
Driven by the interest of reasoning about probabilistic programming languages, we set out to study a notion of unicity of normal forms for them. To provide a tractable proof method for it, we define a property of distribution confluence…
Typical arguments for results like Kleene's Second Recursion Theorem and the existence of self-writing computer programs bear the fingerprints of equational reasoning and combinatory logic. In fact, the connection of combinatory logic and…