Shielding, Apparent Stress, and the Stress Ratio: A Note on Attentional Redistribution in a Phenomenological…

Abstract

We extend a minimal phenomenological model of composite stress by introducing three

quantities:

∑

shielding, apparent stress, and the stress ratio. Composite stress is written as

aieiQi = F, with weights ai ≥ 0, ∑

ai = 1, where ei

is sensitivity and Qi

is the stim-

ulus magnitude of source i. Normalizing by the maximum weight amax = maxi ai

, we define the

shielding factor bi = ai/amax ∈ [0, 1], the normalized effective sensitivity ϵi = bi ei/e0, and the

apparent stress Sapp = F/(e0amaxQ0) = ∑

i Ei with Ei = aieiQi/(e0amaxQ0). We show that (i)

concentrating attention on one stimulus (amax → 1) shields the others and lowers Sapp, while (ii)

the raw stress F changes according to the redistribution of weights. For a shift of weight δ from

a source j to a source k, the change in raw stress is ∆F = δ (ekQk −ejQj ) = δ ejQj (r −1) with

the stress ratio r = ekQk/(ejQj ). Thus F decreases if and only if r < 1, i.e., if the concentration

target is weaker than the displaced source. The apparent and raw stresses are independent: Sapp

can decrease even when F increases. We discuss the implications for attentional shielding (e.g.,

engagement in a demanding activity) and state the limitations of the note.

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BibTeX RIS

BibTeX

@misc{ueda2026shielding,
  title = {{Shielding, Apparent Stress, and the Stress Ratio: A Note on Attentional Redistribution in a Phenomenological Model of Composite Stress}},
  author = {takashi ueda},
  howpublished = {Zenodo},
  year = {2026},
  month = oct,
  doi = {10.5281/zenodo.23503638},
  url = {https://zenodo.org/records/23503638},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Shielding, Apparent Stress, and the Stress Ratio: A Note on Attentional Redistribution in a Phenomenological Model of Composite Stress
AU  - takashi ueda
PY  - 2026
DA  - 2026/10/20
PB  - Zenodo
DO  - 10.5281/zenodo.23503638
UR  - https://zenodo.org/records/23503638
AB  - We extend a minimal phenomenological model of composite stress by introducing three  quantities:  &sum;  shielding, apparent stress, and the stress ratio. Composite stress is written as  i  aieiQi = F, with weights ai ≥ 0, &sum;  i  ai = 1, where ei  is sensitivity and Qi  is the stim-  ulus magnitude of source i. Normalizing by the maximum weight amax = maxi ai  , we define the  shielding factor bi = ai/amax &isin; [0, 1], the normalized effective sensitivity ϵi = bi ei/e0, and the  apparent stress Sapp = F/(e0amaxQ0) = &sum;  i Ei with Ei = aieiQi/(e0amaxQ0). We show that (i)  concentrating attention on one stimulus (amax &rarr; 1) shields the others and lowers Sapp, while (ii)  the raw stress F changes according to the redistribution of weights. For a shift of weight δ from  a source j to a source k, the change in raw stress is ∆F = δ (ekQk −ejQj ) = δ ejQj (r −1) with  the stress ratio r = ekQk/(ejQj ). Thus F decreases if and only if r < 1, i.e., if the concentration  target is weaker than the displaced source. The apparent and raw stresses are independent: Sapp  can decrease even when F increases. We discuss the implications for attentional shielding (e.g.,  engagement in a demanding activity) and state the limitations of the note.
ER  -

Abstract

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