Leonardo's rule, self-similarity and wind-induced stresses in trees

Examining botanical trees, Leonardo da Vinci noted that the total cross-section of branches is conserved across branching nodes. In this Letter, it is proposed that this rule is a consequence of the tree skeleton having a self-similar structure and the branch diameters being adjusted to resist wind-induced loads

Objective diagnostics of tinnitus

Background Tinnitus is the phantom perception of sound reported by around 14% of the population. For over 120 million people worldwide tinnitus is perceived as a major problem. Still, tinnitus is a heterogenous condition with no stratified sub-types or biomarkers for objective assessment. This severely limits the potential for development and evaluation of novel therapies for tinnitus. This thesis aims to I) investigate the relationship between conditions commonly reported by tinnitus patients and II) evaluate the potential of electrophysiology or magnetoencephalography (MEG) to function as an objective biomarker for tinnitus. Methods Studies I-III retrospectively analyzed questionnaire data, in total n = 5 593, collected in the Swedish Tinnitus Outreach Project (STOP) between November 2015 and January 2018. Multivariate logistic regression models were implemented to investigate the association between tinnitus and related conditions - temporomandibular joint (TMJ) pains, hyperacusis and headaches. Study IV used longitudinal data from The Swedish Longitudinal Occupational Survey of Health (SLOSH), in total 20 439 participants, with 53 273 observations. The transition from occasional to constant tinnitus was investigated using Generalized Estimating Equation (GEE) models. The second part of Study IV used ABR data from STOP (n = 405) to evaluate measurements of wave I, III & V amplitude and latency in distinguishing constant from occasional tinnitus, or non-tinnitus controls. Study V recruited n = 22 normal hearing, non-tinnitus participants for optimization of a GPIAS (Gap Pre-pulse Inhibition of Acoustic Startle) protocol for MEG. In this exploratory study sound pulses of 20 ms were presented in 60 or 70 dBA carrier noise with a 50 ms silent gap preceding the pulse by 240, 120, 60 or 0 ms. All MEG were recorded by the Elekta Neuromag TRIUX 306-channel system at NatMEG, Karolinska Institutet. Results TMJ complaints increased to over 30% among those with severe tinnitus, compared to 19% in all participants with tinnitus. For headache, adjusted odds ratios (95% confidence interval) showed an association of OR: 3.8 (2.4-5.9) and a strong association with hyperacusis of OR: 12.1 (7.1-20.6) was found for those with severe tinnitus. Longitudinal analysis indicated that tinnitus progresses towards constant tinnitus and that once established is very unlikely to remit. Changes in the ABR response, particularly wave V latency, distinguished constant from occasional tinnitus and non-tinnitus controls, likely reflecting plastic changes related to this chronification. A GPIAS stimulation protocol with an inter-stimulus interval of 240 ms between silent gap and 90 dBA pulse produced N1-inhibition of ERF responses with much lower variability when compared to traditional EOG responses. Conclusion We identified TMJ complaints and hyperacusis as important factors to consider in future studies of tinnitus. ABR wave V latency can distinguish constant tinnitus from occasional or non-tinnitus at a group level, but is likely not sensitive enough for individual diagnostics. Instead, GPIAS together with MEG is a promising approach to developing a biomarker for tinnitus

Optimal Topological Test for Degeneracies of Real Hamiltonians

We consider adiabatic transport of eigenstates of real Hamiltonians around loops in parameter space. It is demonstrated that loops that map to nontrivial loops in the space of eigenbases must encircle degeneracies. Examples from Jahn-Teller theory are presented to illustrate the test. We show furthermore that the proposed test is optimal.Comment: Minor corrections, accepted in Phys. Rev. Let

Self-thinning and Community Persistence in a Simple Size-structured Dynamical Model of Plant Growth

This paper presents a size-structured dynamical model of plant growth. The model takes the form of a partial differential-integral equation and includes the effects of self-shading by leaves. Closed form solutions are presented for the equilibrium size density distribution. Analytic conditions are derived for community persistence, and the self-thinning exponent is obtained as a function of species characteristics and environmental conditions

Parameterization of the Angular Distribution of Gamma Rays Produced by p-p Interaction in Astronomical Environment

We present the angular distribution of gamma rays produced by proton-proton interactions in parameterized formulae to facilitate calculations in astrophysical environments. The parameterization is derived from Monte Carlo simulations of the up-to-date proton-proton interaction model by Kamae et al. (2005) and its extension by Kamae et al. (2006). This model includes the logarithmically rising inelastic cross section, the diffraction dissociation process and Feynman scaling violation. The extension adds two baryon resonance contributions: one representing the Delta(1232) and the other representing multiple resonances around 1600 MeV/c^2. We demonstrate the use of the formulae by calculating the predicted gamma-ray spectrum for two different cases: the first is a pencil beam of protons following a power law and the second is a fanned proton jet with a Gaussian intensity profile impinging on the surrounding material. In both cases we find that the predicted gamma-ray spectrum to be dependent on the viewing angle.Comment: 8 pages, 7 figures, figure 7 updated, accepted for publication in ApJ, text updated to match changes by the editor, two refs updated from preprints to full journal

Dynamical mean-field theory of indirect magnetic exchange

To analyze the physical properties arising from indirect magnetic exchange between several magnetic adatoms and between complex magnetic nanostructures on metallic surfaces, the real-space extension of dynamical mean-field theory (R-DMFT) appears attractive as it can be applied to systems of almost arbitrary geometry and complexity. While R-DMFT describes the Kondo effect of a single adatom exactly, indirect magnetic (RKKY) exchange is taken into account on an approximate level only. Here, we consider a simplified model system consisting of two magnetic Hubbard sites ("adatoms") hybridizing with a non-interacting tight-binding chain ("substrate surface"). This two-impurity Anderson model incorporates the competition between the Kondo effect and indirect exchange but is amenable to an exact numerical solution via the density-matrix renormalization group (DMRG). The particle-hole symmetric model at half-filling and zero temperature is used to benchmark R-DMFT results for the magnetic coupling between the two adatoms and for the magnetic properties induced in the substrate. In particular, the dependence of the local adatom and the nonlocal adatom-adatom static susceptibilities as well as the magnetic response of the substrate on the distance between the adatoms and on the strength of their coupling with the substrate is studied. We find both, excellent agreement with the DMRG data even on subtle details of the competition between RKKY exchange and the Kondo effect but also complete failure of the R-DMFT, depending on the parameter regime considered. R-DMFT calculations are performed using the Lanczos method as impurity solver. With the real-space extension of the two-site DMFT, we also benchmark a simplified R-DMFT variant.Comment: 14 pages, 8 figure

Parent‐offspring inference in inbred populations

Genealogical relationships are fundamental components of genetic studies. However, it is often challenging to infer correct and complete pedigrees even when genome-wide information is available. For example, inbreeding can obscure genetic differences between individuals, making it difficult to even distinguish first-degree relatives such as parent-offspring from full siblings. Similarly, genotyping errors can interfere with the detection of genetic similarity between parents and their offspring. Inbreeding is common in natural, domesticated, and experimental populations and genotyping of these populations often has more errors than in human data sets, so efficient methods for building pedigrees under these conditions are necessary. Here, we present a new method for parent-offspring inference in inbred pedigrees called specific parent-offspring relationship estimation (spore). spore is vastly superior to existing pedigree-inference methods at detecting parent-offspring relationships, in particular when inbreeding is high or in the presence of genotyping errors, or both. spore therefore fills an important void in the arsenal of pedigree inference tools