# life: apropos of birth-and-death processes, framework for fluctuating times and counting observables in stochastic excursions.

<< ️Many natural systems exhibit dynamics characterized by alternating phases or recurring sets of states. Describing the fluctuations of such systems over stochastic trajectories is necessary across diverse fields, from biological motors to quantum thermal machines. >>

<< ️In an accompanying Letter, (AA) introduced the notion of stochastic excursions−a framework to analyze out of equilibrium processes via sub-trajectories. Through counting observables, this framework captures finite-time fluctuations and trajectory-level behavior, which provides insights into thermodynamical trade-offs between thermodynamic quantities of interest, such as entropy production and dynamical activity. >>

<< ️In this work, (AA) enhance this formalism by providing a suite of technical results on how to efficiently compute excursion-related quantities. (Their) analytical results provide explicit formulas for general moments of counting variables and excursion duration, as well as their covariance and conditional moments. (They) show that excursion statistics recover full counting statistics results, and uncover a relation between fluctuations of counting observables at single-excursion level and the steady state diffusion coefficient (noise). >> 

<< ️(AA) also discuss a fluctuation theorem for individual excursions and show that it implies a modified thermodynamic uncertainty relation at the excursion level. In addition, (They) explore how analyzing excursions and using the results developed here can yield insights into three problems of interest: the three-qubit absorption refrigerator, cellular sensing, and birth-and-death processes. >>

Guilherme Fiusa, Pedro E. Harunari, Abhaya S. Hegde, et al. Framework for fluctuating times and counting observables in stochastic excursions.

Phys. Rev. E 114, 024129. Aug 13, 2026.

https://journals.aps.org/pre/abstract/10.1103/jydr-1853

arXiv: 2506.05160v3 [cond-mat.stat-mech]. Aug 19, 2026.

https://arxiv.org/abs/2506.05160

Also: Guilherme Fiusa, Pedro E. Harunari, Abhaya S. Hegde, et al. Counting observables in stochastic excursions. Phys. Rev. E 114, L022102 (2026). 

https://journals.aps.org/pre/abstract/10.1103/1blp-2b27

Also: walk, walking, uncertainty, fluctuations, random, noise, behav, Nomads, in https://www.inkgmr.net/kwrds.html 

Keywords: walk, walking, noise, uncertainty, behavior, fluctuations, randomness, stochasticity, stochastic excursions, Nomads. 

# brain: apropos of persistent exploratory predisposition, chaotic pigeons are helping redefine what we know about learning.

<< ️Pigeons seem to defy a century-old psychology law about how rewards and consequences help us learn. >>

<< ️New research suggests the birds themselves avoid stability in their decision-making, instead choosing to live “at the edge of chaos.” As model species for learning and behavior, these birds are helping researchers test a century-old law about how humans and other creatures learn. >>

<< ️When learning something new, people and animals alike tend to repeat behaviors that are rewarded. First proposed by Edward Thorndike in 1898, this principle is so well established in psychology that it's become known as the law of effect. But the law implies that beyond making a behavior more frequent, rewards also make it more consistent: reducing variability in the specific way behaviors are performed over time. >>

<< ️Edward A. Wasserman and his colleagues decided to put it to the test in pigeons—a species that has been integral to the study of learning at the university’s Comparative Cognition Laboratory for more than 50 years. And the study’s results, published in the Journal of Experimental Psychology: Animal Learning and Cognition, suggest these birds experience variability as the spice of life. >>

<< ️You could argue the birds are just utterly resistant to locking into anything stable. >> Edward A. Wasserman.

<< ️this paper leaves open many questions about the [neurological] mechanisms for future scientists to explore. >> Aaron Blaisdell.

K. R. Callaway, Sarah Lewin Frasier. Chaotic pigeons are helping redefine what we know about learning. SciAm. Jun 30, 2026. 

https://www.scientificamerican.com/article/chaotic-pigeons-are-helping-redefine-what-we-know-about-learning

Wasserman E.A., Orr O.R.P., Li S. Variability, stability, and the law of effect. J. of Exp. Psychol: Animal Learning and Cognition, 52(3), 129–138. Jul 2026. 

https://psycnet.apa.org/record/2027-47688-001

Also: brain, neuro, behav, curiosity, game, Nomads, in https://www.inkgmr.net/kwrds.html 

Keywords: brain, behavior, curiosity, games, Nomads.

# life: the role played by women in shaping human evolution.

<< ️(AA) have used ancient DNA to reveal that hunter-gatherers in one part of Europe survived for thousands of years longer than anywhere else on the continent—and have uncovered the pivotal role of women in the process >>

<< ️Ancient DNA studies often bring to light unexpected pages of our past. We might anticipate finding the unexpected when analyzing samples from unexplored or peripheral regions of the globe. But here we are looking at the heartland of Europe, making these results even more striking. It's a testament to the power of ancient DNA studies that findings like these can still surprise us. This study has also brought to light the crucial role played by women in the transmission of knowledge from the incoming farming communities to the local hunter-gatherers. Thanks to ancient DNA studies, we can not only uncover the past but also give voice to the invaluable but often overlooked role played by women in shaping human evolution. >> Maria Pala. 

Gaby Clark, Robert Egan. Ancient DNA suggests hunter-gatherers in Europe's lowlands endured until 2500 BCE. University of Huddersfield. http://www.hud.ac.uk  Feb 11, 2026.

https://phys.org/news/2026-02-ancient-dna-hunter-europe-lowlands.html 

Olalde, I., Altena, E., Bourgeois, Q. et al. Lasting Lower Rhine–Meuse forager ancestry shaped Bell Beaker expansion. Nature (2026). https://doi.org/10.1038/s41586-026-10111-8

Also: Nomads, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: Nomads, transitions, life