High-order Hu moment invariant functions have always been required to solve a variety of problems. Up to this point, there was no generalized approach to extend the first six Hu moment invariants to higher orders. Therefore, this paper presents a generalized algorithm to determine rotationally invariant Hu moment invariants of any desired order, which are invariant to scaling, translation and r...

Complex regulatory programs control cell adaptation to environmental changes by setting condition-specific proteomes. In balanced growth, bacterial protein abundances depend on the dilution rate, transcript abundances and transcript-specific translation efficiencies. We revisited the current theory claiming the invariance of bacterial translation efficiency. By integrating genome-wide transcrip...

Once one has these two properties, one obtains several additional properties for free, such as boundedness on L(R) for all 1 < p < ∞; also T and T ∗ both map L to BMO. However, it is not always easy to verify these properties in practice. The singular kernel properties are usually not too difficult, as the kernel can often be expressed directly, and then estimated pointwise in a fairly straight...

We give a new proof of the KAM theorem for analytic Hamiltonians. The proof is inspired by a quantum field theory formulation of the problem and is based on a renormalization group argument treating the small denominators inductively scale by scale. The crucial cancellations of resonances are shown to follow from the Ward identities expressing the translation invariance of the corresponding fie...

Entropy is a measure of the uncertainty associated with an uncertain variable. So far, entropy, quadratic entropy and sine entropy have been proposed for uncertain variables. This paper will propose a triangular entropy for uncertain variables, and verify its properties such as translation invariance and positive linearity.

We show that strongly monotone systems of ordinary differential equations which have a certain translation-invariance property are so that all solutions converge to a unique equilibrium. The result may be seen as a dual of a well-known theorem of Mierczynski for systems that satisfy a conservation law. An application to a reaction of interest in biochemistry is provided as an illustration.

Discrete morphological operations with line segments are notoriously hard to implement. In this paper we study different possible implementations of the line structuring element, compare them, and examine their rotation and translation invariance in the continuous-domain sense. That is, we are interested in obtaining a morphological operator that is invariant to rotations and translations of th...

The dependence of various types of linear signals on the phase profile of broadband optical pulses is examined using fundamental time translation invariance symmetry of multipoint correlation functions. The frequency-domain wave-mixing analysis presented here unifies several arguments made earlier with respect to the conditions whereby coherent control schemes may be used.