Multi-hypothesis comparison of Farquhar and Collatz photosynthesis models reveals the unexpected influence of empirical assumptions at leaf and global scales. [PDF]
Walker AP +10 more
europepmc +1 more source
Behavioral factors associated with SARS-CoV-2 infection. [PDF]
Bager MD +14 more
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The Olfactory System of <i>Dolichogenidea gelechiidivoris</i> (Marsh) (Hymenoptera: Braconidae), a Natural Enemy of <i>Tuta absoluta</i> (Meyrick) (Lepidoptera: Gelechiidae). [PDF]
Yan SY +9 more
europepmc +1 more source
A Complete Proof of the Collatz Conjecture Using Generator Functions
We present a complete proof of the Collatz conjecture using a novel approach based on generator functions. By analyzing the inverse mappings of the Collatz function through carefully defined generator operations, we establish that all natural numbers must eventually reach 1 under the Collatz iteration.
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Increased overwintering temperature reduces reproductive success of the solitary bee species Osmia bicornis. [PDF]
Müller S +4 more
europepmc +1 more source
DeepLBCEPred: A Bi-LSTM and multi-scale CNN-based deep learning method for predicting linear B-cell epitopes. [PDF]
Qi Y, Zheng P, Huang G.
europepmc +1 more source
Criteria codes for unrecognized stroke/TIA patients by Emergency Medical Services dispatchers in Copenhagen, Denmark. [PDF]
Andreasen PB +4 more
europepmc +1 more source
A retrospective study on immune-related pneumonitis in patients with non-small-cell lung cancer undergoing treatment with PD-1/PD-L1 inhibitors. [PDF]
Yakymenko D, Skougaard K.
europepmc +1 more source
A Local Lyapunov Function for the Collatz Map on n ≡ 6 (mod 8)
We prove an explicit formula for the number of consecutive odd steps of the Collatz map for integers n ≡ 6 (mod 8). For n = 8m + 6, the number of iterations of T(k) = (3k+1)/2 before reaching an even value is exactly ν₂(m+1), where ν₂ is the 2-adic valuation.
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