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1. On the Location of the Minimizer of the Sum of Two Strongly Convex Functions

   https://doi.org/10.1109/CDC.2018.8619735  

   Kuwaranancharoen, Kananart; Sundaram, Shreyas (December 2018, 2018 IEEE Conference on Decision and Control (CDC))

   The problem of finding the minimizer of a sum of convex functions is central to the field of distributed optimization. Thus, it is of interest to understand how that minimizer is related to the properties of the individual functions in the sum. In this paper, we provide an upper bound on the region containing the minimizer of the sum of two strongly convex functions. We consider two scenarios with different constraints on the upper bound of the gradients of the functions. In the first scenario, the gradient constraint is imposed on the location of the potential minimizer, while in the second scenario, the gradient constraint is imposed on a given convex set in which the minimizers of two original functions are embedded. We characterize the boundaries of the regions containing the minimizer in both scenarios. 

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2. Possibilities of applying the concept of “winter city” in the Russian Arctic (on the example of the city of Nadym).

   https://doi.org/10.25283/2223-4594-2021-2-291-303  

   Fedorov, Roman Y; Sizov, Oleg S; Kuklina, Vera V; Lobanov, Andrei A; Soromotin, Andrei V; Pechkin, Alexander S; Pechkina, Yulia A; Esau, Igor N (April 2021, Arctica)

   null (Ed.)

   On example of the city of Nadym, located in the Yamalo-Nenets Autonomous Area, the authors consider the socio-ecological problems of the development of green, blue and white open urban spaces. The research approach presented in the article is based on the study of a multifaceted complex of urban social and natural systems in their integrated unity, not just as public places, but as biomes — highly integrated urban ecosystems. A posteriori the researchers based on the materials of interviews conducted in 2020 with experts who in different years took part in the study or planned the development of the open urban spaces in Nadym, as well as on the analysis of available publications on this topic and publicly available data. The study found that factors such as the short summer, during which many residents leave the city, as well as the prevalence of freezing temperatures for almost eight months, in fact, transform the green and blue spaces of Nadym into white. This situation indicates the advisability of a more active appeal to the concept of a “winter city” in the development of the city urban environment. The application of the concept principles can be in demand in the process of creating more comfortable living conditions and spatial mobility of the Nadym residents, as well as for developing the recreational opportunities of the city open spaces and integrating them into the natural environment surrounding the city, which in general can be considered as one of the factors for the sustainable development of the city and the formation of post-industrial features in its socio-economic life. 

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3. Onset of the wave turbulence description of the longtime behavior of the nonlinear Schrödinger equation

   https://doi.org/10.1007/s00222-021-01039-z  

   Buckmaster, T.; Germain, P.; Hani, Z.; Shatah, J. (September 2021, Inventiones mathematicae)

   null (Ed.)

   Abstract Consider the cubic nonlinear Schrödinger equation set on a d -dimensional torus, with data whose Fourier coefficients have phases which are uniformly distributed and independent. We show that, on average, the evolution of the moduli of the Fourier coefficients is governed by the so-called wave kinetic equation , predicted in wave turbulence theory, on a nontrivial timescale. 

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4. The neuroecology of the water-to-land transition and the evolution of the vertebrate brain

   https://doi.org/10.1098/rstb.2020.0523  

   MacIver, Malcolm A.; Finlay, Barbara L. (February 2022, Philosophical Transactions of the Royal Society B: Biological Sciences)

   The water-to-land transition in vertebrate evolution offers an unusual opportunity to consider computational affordances of a new ecology for the brain. All sensory modalities are changed, particularly a greatly enlarged visual sensorium owing to air versus water as a medium, and expanded by mobile eyes and neck. The multiplication of limbs, as evolved to exploit aspects of life on land, is a comparable computational challenge. As the total mass of living organisms on land is a hundredfold larger than the mass underwater, computational improvements promise great rewards. In water, the midbrain tectum coordinates approach/avoid decisions, contextualized by water flow and by the animal’s body state and learning. On land, the relative motions of sensory surfaces and effectors must be resolved, adding on computational architectures from the dorsal pallium, such as the parietal cortex. For the large-brained and long-living denizens of land, making the right decision when the wrong one means death may be the basis of planning, which allows animals to learn from hypothetical experience before enactment. Integration of value-weighted, memorized panoramas in basal ganglia/frontal cortex circuitry, with allocentric cognitive maps of the hippocampus and its associated cortices becomes a cognitive habit-to-plan transition as substantial as the change in ecology. This article is part of the theme issue ‘Systems neuroscience through the lens of evolutionary theory’. 

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5. The Influence of the Mechanical Compliance of a Substrate on the Morphology of Nanoporous Gold Thin Films

   https://doi.org/10.3390/nano14090758  

   Shahriar, Sadi; Somayajula, Kavya; Winkeljohn, Conner; Mason, Jeremy K; Seker, Erkin (May 2024, Nanomaterials)

   Nanoporous gold (np-Au) has found its use in applications ranging from catalysis to biosensing, where pore morphology plays a critical role in performance. While the morphology evolution of bulk np-Au has been widely studied, knowledge about its thin-film form is limited. This work hypothesizes that the mechanical compliance of the thin film substrate can play a critical role in the morphology evolution. Via experimental and finite-element-analysis approaches, we investigate the morphological variation in np-Au thin films deposited on compliant silicone (PDMS) substrates of a range of thicknesses anchored on rigid glass supports and compare those to the morphology of np-Au deposited on glass. More macroscopic (10 s to 100 s of microns) cracks and discrete islands form in the np-Au films on PDMS compared to on glass. Conversely, uniformly distributed microscopic (100 s of nanometers) cracks form in greater numbers in the np-Au films on glass than those on PDMS, with the cracks located within the discrete islands. The np-Au films on glass also show larger ligament and pore sizes, possibly due to higher residual stresses compared to the np-Au/PDMS films. The effective elastic modulus of the substrate layers decreases with increasing PDMS thickness, resulting in secondary np-Au morphology effects, including a reduction in macroscopic crack-to-crack distance, an increase in microscopic crack coverage, and a widening of the microscopic cracks. However, changes in the ligament/pore widths with PDMS thickness are negligible, allowing for independent optimization for cracking. We expect these results to inform the integration of functional np-Au films on compliant substrates into emerging applications, including flexible electronics. 

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