We prove the existence of novel, shock-fronted travelling wave solutions to a model of wound healing angiogenesis studied in Pettet et al., IMA J. Math. App. Med., 17, 2000. In this work, the authors showed that for certain parameter values, a hetero...
Several studies question the adaptive value of female preferences for older males. Theory and evidence show that older males carry more deleterious mutations in their sperm than younger males carry. These mutations are not visible to females choosing...
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The largest coefficient (in absolute value) of a cyclotomic polynomial $Φ_n$ is called its height $A(n)$. In case $p$ is a fixed prime it turns out that as $q$ and $r$ range over all primes satisfying $p<q<r$, the height $A(pqr)$ assumes a maximum $...
For a fixed prime $p$, the maximum coefficient (in absolute value) $M(p)$ of the cyclotomic polynomial $Φ_{pqr}(x)$, where $r$ and $q$ are free primes satisfying $r>q>p$ exists. Sister Beiter conjectured in 1968 that $M(p)\le(p+1)/2$. In 2009 Gallot...
Model-free reinforcement learning methods lack an inherent mechanism to impose behavioural constraints on the trained policies. Although certain extensions exist, they remain limited to specific types of constraints, such as value constraints with ad...
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Deviation generally refers to a departure or divergence from an expected or typical pattern, behavior, value, or standard. It suggests a variation from the norm or an alteration from an established course …
The deviation of a value of x is the difference between it and the mean of the sample. Each deviation is then squared.
Reinforcement Learning (RL) can model complex behavior policies for goal-directed sequential decision making tasks. A hallmark of RL algorithms is Temporal Difference (TD) learning: value function for the current state is moved towards a bootstrapped...
We consider a communication network over which transmissions must fulfill the so-called token bucket traffic specification, with a rollout (i.e., predictive) controller that both schedules transmissions and computes the corresponding control values....
Nov 6, 2023 · In my case, these values are 0.110 and 0.023, respectively. Is there any sort of rule of thumb as to how much the variance should exceed the mean, before going to the effort of running a …
Theoretical calculations of solvation contribution to hole energy in a polynucleotide chain give very low hole mobility values at zero temperature, μ< 10^{-3} cm^2/(V s). We calculated hole mobility at physiological temperature for the Poly G/Poly C...
The quantum theory of rotation angles (S. M. Barnett and D. T. Pegg, Phys. Rev. A, 41, 3427-3425 (1990)) is generalised to non-integer values of the orbital angular momentum. This requires the introduction of an additional parameter, the orientatio...
One of the most valuable assets of an organization is its organizational data. The analysis and mining of this potential hidden treasure can lead to much added-value for the organization. Process mining is an emerging area that can be useful in helpi...
This note provides an effective lower bound for the number of primes in the quadratic progression $p=n^2+1 \leq x$ as $x \to \infty$....
The recent technique for estimating lower bounds of the prime counting function $π(x)=#\{p \leq x: p\text{ prime}\}$ by means of the irrationality measures $μ(ζ(s)) \geq 2$ of special values of the zeta function claims that $π(x) \gg \log \log x/...
It is shown that the Mean Value Theorem for arithmetic functions, and simple properties of the zeta function are sufficient to assemble proofs of the Prime Number Theorem, and Dirichlet Theorem. These are among the simplest proofs of the asymptotic f...
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We study the budget map and the indirect utility function of a parametric consumer problem in a Banach space setting by some advanced tools from set-valued and variational analysis. The Lipschitz-likeness and differentiability properties of the budge...