Observational equality: now for good

Building on the recent extension of dependent type theory with a universe of definitionally proof-irrelevant types, we introduce TTobs, a new type theory based on the setoidal interpretation of dependent type theory. TTobs equips every type with an identity relation that satisfies function extensionality, propositional extensionality, and definitional uniqueness of identity proofs (UIP). Compared to other existing proposals to enrich dependent type theory with these principles, our theory features a notion of reduction that is normalizing and provides an algorithmic canonicity result, which we formally prove in Agda using the logical relation framework of Abel et al. Our paper thoroughly develops the meta-theoretical properties of TTobs, such as the decidability of the conversion and of the type checking, as well as consistency. We also explain how to extend our theory with quotient types, and we introduce a setoidal version of Swan's Id types that turn it into a proper extension of MLTT with inductive equality.

Diversity Scaling Analysis of Chinese Gut Microbiomes Across Ethnicities and Lifestyles

Diversity scaling (changes) of human gut microbiome is important because it measures the inter-individual heterogeneity of diversity and other important parameters of population-level diversity. Understanding the heterogeneity of microbial diversity can be used as a reference for the personalized medicine of microbiome-associated diseases. Similar to diversity per se, diversity scaling may also be influenced by host factors, especially lifestyles and ethnicities. Nevertheless, this important topic regarding Chinese populations has not been addressed, to our best knowledge. Here, we fill the gap by applying a recent extension to the classic species–area relationship (SAR), i.e., diversity–area relationship (DAR), to reanalyze a large dataset of Chinese gut microbiomes covering the seven biggest Chinese ethnic groups (covering > 95% Chinese) living rural and urban lifestyles. Four DAR profiles were constructed to investigate the diversity scaling, diversity overlap, potential maximal diversity, and the ratio of local to global diversity of Chinese gut microbiomes. We discovered the following: (i) The diversity scaling parameters (z) at various taxon levels are little affected by either ethnicity or lifestyles, as exhibited by less than 0.5% differences in pairwise comparisons. (ii) The maximal accrual diversity (potential diversity) exhibited difference in only about 5% of pairwise comparisons, and all of the differences occurred in ethnicity comparisons (i.e., lifestyles had no effects). (iii) Ethnicity seems to have stronger effects than lifestyles across all taxon levels, and this may reflect the reality that China has been experiencing rapid urbanization in the last few decades, while the ethnic-related genetic background may change relatively little during the same period.

TWO-DIMENSIONAL COLOUR APPEARANCE SCALES FOR COLOUR STIMULI HAVING HIGH DYNAMIC RANGE

New colour appearance scales close to daily experience and image quality enhancement are highly desired including whiteness, blackness, vividness and depth. This article describes a new experiment to accumulate the data under HDR (high dynamic range) conditions. The data were then used to test the performance of different colour appearance scales such as CIELAB and CAM16-UCS plus the recent extension by Berns’ Vab*, Dab*. The results showed those Berns’ scales gave reasonable performance. However, there was no scale capable of predicting colour appearance data covering a wide dynamic range. New scales were developed based on the absolute scales of brightness and colourfulness of CAM16-UCS and gave accurate prediction to the data.

Beyond Topological Persistence: Starting from Networks

Persistent homology enables fast and computable comparison of topological objects. We give some instances of a recent extension of the theory of persistence, guaranteeing robustness and computability for relevant data types, like simple graphs and digraphs. We focus on categorical persistence functions that allow us to study in full generality strong kinds of connectedness—clique communities, k-vertex, and k-edge connectedness—directly on simple graphs and strong connectedness in digraphs.

Numerical Application of Effective Thickness Approach to Box Aluminium Sections

The ultimate behaviour of aluminium members subjected to uniform compression or bending is strongly influenced by local buckling effects which occur in the portions of the section during compression. In the current codes, the effective thickness method (ETM) is applied to evaluate the ultimate resistance of slender cross-sections affected by elastic local buckling. In this paper, a recent extension of ETM is presented to consider the local buckling effects in the elastic-plastic range and the interaction between the plate elements constituting the cross-section. The theoretical results obtained with this approach, applied to box-shaped aluminium members during compression or in bending, are compared with the experimental tests provided in the scientific literature. It is observed that the ETM is a valid and accurate tool for predicting the maximum resistance of box-shaped aluminium members during compression or in bending.

New colour appearance scales under high dynamic range conditions

New colour appearance scales close to daily experience and image quality enhancement are highly desired including whiteness, blackness, vividness and depth. This article describes a new experiment to accumulate the data under HDR (high dynamic range) conditions. The data were then used to test the performance of different colour appearance scales such as CIELAB and CAM16-UCS plus the recent extension by Berns' Vab*, Dab*. The results showed those Berns' scales gave a reasonable performance. However, it was found no scale is capable of predicting colour appearance data covering a wide dynamic range. New scales were developed based on the absolute scales of brightness and colourfulness of CAM16-UCS and gave accurate predictions to the data.

Path-integral approximations to quantum dynamics

Imaginary-time path-integral or ‘ring-polymer’ methods have been used to simulate quantum (Boltzmann) statistical properties since the 1980s. This article reviews the more recent extension of such methods to simulate quantum dynamics, summarising the chain of approximations that links practical path-integral methods, such as centroid molecular dynamics (CMD) and ring-polymer molecular dynamics (RPMD), to the exact quantum Kubo time-correlation function. We focus on single-surface Born–Oppenheimer dynamics, using the infrared spectrum of water as an illustrative example, but also survey other recent applications and practical techniques, as well as the limitations of current methods and their scope for future development. Graphic abstract

Nanomaterials in Skin Regeneration and Rejuvenation

Skin is the external part of the human body; thus, it is exposed to outer stimuli leading to injuries and damage, due to being the tissue mostly affected by wounds and aging that compromise its protective function. The recent extension of the average lifespan raises the interest in products capable of counteracting skin related health conditions. However, the skin barrier is not easy to permeate and could be influenced by different factors. In the last decades an innovative pharmacotherapeutic approach has been possible thanks to the advent of nanomedicine. Nanodevices can represent an appropriate formulation to enhance the passive penetration, modulate drug solubility and increase the thermodynamic activity of drugs. Here, we summarize the recent nanotechnological approaches to maintain and replace skin homeostasis, with particular attention to nanomaterials applications on wound healing, regeneration and rejuvenation of skin tissue. The different nanomaterials as nanofibers, hydrogels, nanosuspensions, and nanoparticles are described and in particular we highlight their main chemical features that are useful in drug delivery and tissue regeneration.

Using distance sampling with camera traps to estimate the density of group-living and solitary mountain ungulates

Throughout the Himalaya, mountain ungulates are threatened by hunting for meat and body parts, habitat loss, and competition with livestock. Accurate population estimates are important for conservation management but most of the available methods to estimate ungulate densities are difficult to implement in mountainous terrain. Here, we tested the efficacy of the recent extension of the point transect method, using camera traps for estimating density of two mountain ungulates: the group-living Himalayan blue sheep or bharal Pseudois nayaur and the solitary Himalayan musk deer Moschus leucogaster. We deployed camera traps in 2017–2018 for the bharal (summer: 21 locations; winter: 25) in the trans-Himalayan region (3,000–5,000 m) and in 2018–2019 for the musk deer (summer: 30 locations; winter: 28) in subalpine habitats (2,500–3,500 m) in the Upper Bhagirathi basin, Uttarakhand, India. Using distance sampling with camera traps, we estimated the bharal population to be 0.51 ± SE 0.1 individuals/km2 (CV = 0.31) in summer and 0.64 ± SE 0.2 individuals/km2 (CV = 0.37) in winter. For musk deer, the estimated density was 0.4 ± SE 0.1 individuals/km2 (CV = 0.34) in summer and 0.1 ± SE 0.05 individuals/km2 (CV = 0.48) in winter. The high variability in these estimates is probably a result of the topography of the landscape and the biology of the species. We discuss the potential application of distance sampling with camera traps to estimate the density of mountain ungulates in remote and rugged terrain, and the limitations of this method.