On Convergence Properties of Shannon Entropy

Convergence properties of Shannon Entropy are studied. In the differential setting, it is shown that weak convergence of probability measures, or convergence in distribution, is not enough for convergence of the associated differential entropies. A general result for the desired differential entropy convergence is provided, taking into account both compactly and uncompactly supported densities. Convergence of differential entropy is also characterized in terms of the Kullback-Liebler discriminant for densities with fairly general supports, and it is shown that convergence in variation of probability measures guarantees such convergence under an appropriate boundedness condition on the densities involved. Results for the discrete setting are also provided, allowing for infinitely supported probability measures, by taking advantage of the equivalence between weak convergence and convergence in variation in this setting.Comment: Submitted to IEEE Transactions on Information Theor

Mineral analysis reveals extreme manganese concentrations in wild harvested and commercially available edible termites

Open Access Journal; Published online: 09 April 2020Termites are widely used as a food resource, particularly in Africa and Asia. Markets for insects as food are also expanding worldwide. To inform the development of insect-based foods, we analysed selected minerals (Fe-Mn-Zn-Cu-Mg) in wild-harvested and commercially available termites. Mineral values were compared to selected commercially available insects. Alate termites, of the genera Macrotermes and Odontotermes, showed remarkably high manganese (Mn) content (292–515 mg/100 gdw), roughly 50–100 times the concentrations detected in other insects. Other mineral elements occur at moderate concentrations in all insects examined. On further examination, the Mn is located primarily in the abdomens of the Macrotermes subhyalinus; with scanning electron microscopy revealing small spherical structures highly enriched for Mn. We identify the fungus comb, of Macrotermes subhyanus, as a potential biological source of the high Mn concentrations. Consuming even small quantities of termite alates could exceed current upper recommended intakes for Mn in both adults and children. Given the widespread use of termites as food, a better understanding the sources, distribution and bio-availability of these high Mn concentrations in termite alates is needed

High Light Induced Disassembly of Photosystem II Supercomplexes in Arabidopsis Requires STN7-Dependent Phosphorylation of CP29

Photosynthetic oxidation of water and production of oxygen by photosystem II (PSII) in thylakoid membranes of plant chloroplasts is highly affected by changes in light intensities. To minimize damage imposed by excessive sunlight and sustain the photosynthetic activity PSII, organized in supercomplexes with its light harvesting antenna, undergoes conformational changes, disassembly and repair via not clearly understood mechanisms. We characterized the phosphoproteome of the thylakoid membranes from Arabidopsis thaliana wild type, stn7, stn8 and stn7stn8 mutant plants exposed to high light. The high light treatment of the wild type and stn8 caused specific increase in phosphorylation of Lhcb4.1 and Lhcb4.2 isoforms of the PSII linker protein CP29 at five different threonine residues. Phosphorylation of CP29 at four of these residues was not found in stn7 and stn7stn8 plants lacking the STN7 protein kinase. Blue native gel electrophoresis followed by immunological and mass spectrometric analyses of the membrane protein complexes revealed that the high light treatment of the wild type caused redistribution of CP29 from PSII supercomplexes to PSII dimers and monomers. A similar high-light-induced disassembly of the PSII supercomplexes occurred in stn8, but not in stn7 and stn7stn8. Transfer of the high-light-treated wild type plants to normal light relocated CP29 back to PSII supercomplexes. We postulate that disassembly of PSII supercomplexes in plants exposed to high light involves STN7-kinase-dependent phosphorylation of the linker protein CP29. Disruption of this adaptive mechanism can explain dramatically retarded growth of the stn7 and stn7stn8 mutants under fluctuating normal/high light conditions, as previously reported

Differential Phosphorylation of Ribosomal Proteins in Arabidopsis thaliana Plants during Day and Night

Protein synthesis in plants is characterized by increase in the translation rates for numerous proteins and central metabolic enzymes during the day phase of the photoperiod. The detailed molecular mechanisms of this diurnal regulation are unknown, while eukaryotic protein translation is mainly controlled at the level of ribosomal initiation complexes, which also involves multiple events of protein phosphorylation. We characterized the extent of protein phosphorylation in cytosolic ribosomes isolated from leaves of the model plant Arabidopsis thaliana harvested during day or night. Proteomic analyses of preparations corresponding to both phases of the photoperiod detected phosphorylation at eight serine residues in the C-termini of six ribosomal proteins: S2-3, S6-1, S6-2, P0-2, P1 and L29-1. This included previously unknown phosphorylation of the 40S ribosomal protein S6 at Ser-231. Relative quantification of the phosphorylated peptides using stable isotope labeling and mass spectrometry revealed a 2.2 times increase in the day/night phosphorylation ratio at this site. Phosphorylation of the S6-1 and S6-2 variants of the same protein at Ser-240 increased by the factors of 4.2 and 1.8, respectively. The 1.6 increase in phosphorylation during the day was also found at Ser-58 of the 60S ribosomal protein L29-1. It is suggested that differential phosphorylation of the ribosomal proteins S6-1, S6-2 and L29-1 may contribute to modulation of the diurnal protein synthesis in plants

A Protein Phosphorylation Threshold for Functional Stacking of Plant Photosynthetic Membranes

Phosphorylation of photosystem II (PSII) proteins affects macroscopic structure of thylakoid photosynthetic membranes in chloroplasts of the model plant Arabidopsis. In this study, light-scattering spectroscopy revealed that stacking of thylakoids isolated from wild type Arabidopsis and the mutant lacking STN7 protein kinase was highly influenced by cation (Mg++) concentrations. The stacking of thylakoids from the stn8 and stn7stn8 mutants, deficient in STN8 kinase and consequently in light-dependent phosphorylation of PSII, was increased even in the absence of Mg++. Additional PSII protein phosphorylation in wild type plants exposed to high light enhanced Mg++-dependence of thylakoid stacking. Protein phosphorylation in the plant leaves was analyzed during day, night and prolonged darkness using three independent techniques: immunoblotting with anti-phosphothreonine antibodies; Diamond ProQ phosphoprotein staining; and quantitative mass spectrometry of peptides released from the thylakoid membranes by trypsin. All assays revealed dark/night-induced increase in phosphorylation of the 43 kDa chlorophyll-binding protein CP43, which compensated for decrease in phosphorylation of the other PSII proteins in wild type and stn7, but not in the stn8 and stn7stn8 mutants. Quantitative mass spectrometry determined that every PSII in wild type and stn7 contained on average 2.5±0.1 or 1.4±0.1 phosphoryl groups during day or night, correspondingly, while less than every second PSII had a phosphoryl group in stn8 and stn7stn8. It is postulated that functional cation-dependent stacking of plant thylakoid membranes requires at least one phosphoryl group per PSII, and increased phosphorylation of PSII in plants exposed to high light enhances stacking dynamics of the photosynthetic membranes

Reduced expression of the polymeric immunoglobulin receptor in pancreatic and periampullary adenocarcinoma signifies tumour progression and poor prognosis

The polymeric immunoglobulin receptor (pIgR) is a key component of the mucosal immune system that mediates epithelial transcytosis of immunoglobulins. High pIgR expression has been reported to correlate with a less aggressive tumour phenotype and an improved prognosis in several human cancer types. Here, we examined the expression and prognostic significance of pIgR in pancreatic and periampullary adenocarcinoma. The study cohort encompasses a consecutive series of 175 patients surgically treated with pancreaticoduodenectomy for pancreatic and periampullary adenocarcinoma in Malmö and Lund University Hospitals, Sweden, between 2001-2011. Tissue microarrays were constructed from primary tumours (n = 175) and paired lymph node metastases (n = 105). A multiplied score was calculated from the fraction and intensity of pIgR staining. Classification and regression tree analysis was used to select the prognostic cut-off. Unadjusted and adjusted hazard ratios (HR) for death and recurrence within 5 years were calculated. pIgR expression could be evaluated in 172/175 (98.3%) primary tumours and in 96/105 (91.4%) lymph node metastases. pIgR expression was significantly down-regulated in lymph node metastases as compared with primary tumours (p = 0.018). Low pIgR expression was significantly associated with poor differentiation grade (p < 0.001), perineural growth (p = 0.027), lymphatic invasion (p = 0.016), vascular invasion (p = 0.033) and infiltration of the peripancreatic fat (p = 0.039). In the entire cohort, low pIgR expression was significantly associated with an impaired 5-year survival (HR = 2.99, 95% confidence interval (CI) 1.71-5.25) and early recurrence (HR = 2.89, 95% CI 1.67-4.98). This association remained significant for survival after adjustment for conventional clinicopathological factors, tumour origin and adjuvant treatment (HR = 1.98, 95% CI 1.10-3.57). These results demonstrate, for the first time, that high tumour-specific pIgR expression signifies a more favourable tumour phenotype and that low expression independently predicts a shorter survival in patients with pancreatic and periampullary cancer. The mechanistic basis for the putative tumour suppressing properties of pIgR in these cancers merits further study

Fractal-dimensional properties of subordinators

This work looks at the box-counting dimension of sets related to subordinators (non-decreasing Lévy processes). It was recently shown in Savov (Electron Commun Probab 19:1–10, 2014) that almost surely limδ→0U(δ)N(t,δ)=t , where N(t,δ) is the minimal number of boxes of size at most δ needed to cover a subordinator’s range up to time t, and U(δ) is the subordinator’s renewal function. Our main result is a central limit theorem (CLT) for N(t,δ) , complementing and refining work in Savov (2014). Box-counting dimension is defined in terms of N(t,δ) , but for subordinators we prove that it can also be defined using a new process obtained by shortening the original subordinator’s jumps of size greater than δ . This new process can be manipulated with remarkable ease in comparison with N(t,δ) , and allows better understanding of the box-counting dimension of a subordinator’s range in terms of its Lévy measure, improving upon Savov (2014, Corollary 1). Further, we shall prove corresponding CLT and almost sure convergence results for the new process

Uniform Boundary Harnack Principle for Rotationally Symmetric Levy processes in General Open Sets

In this paper we prove the uniform boundary Harnack principle in general open sets for harmonic functions with respect to a large class of rotationally symmetric purely discontinuous L\'evy processes.Comment: 21 Page

Structure and variability of the Denmark Strait Overflow: Model and observations

We report on a combined modeling and observational effort to understand the Denmark Strait Overflow (DSO). Four cruises over the course of 3 years mapped hydrographic properties and velocity fields with high spatial resolution. The observations reveal the mean path of the dense water, as well as the presence of strong barotropic flows, energetic variability, and strong bottom friction and entrainment. A regional sigma coordinate numerical model of interbasin exchange using realistic bottom topography and an overflow forced only by an upstream reservoir of dense fluid is compared with the observations and used to further investigate these processes. The model successfully reproduces the volume transport of dense water at the sill, as well as the 1000-m descent of the dense water in the first 200 km from the sill and the intense eddies generated at 1–3 day intervals. Hydraulic control of the mean flow is indicated by a region supercritical to long gravity waves in the dense layer located approximately 100 km downstream of the sill in both model and observations. In addition, despite the differences in surface forcing, both model and observations exhibit similar transitions from mostly barotropic flow at the sill to a bottom-trapped baroclinic flow downstream, indicating the dominant role of the overflow in determining the full water column dynamics

Large-deviation principles, stochastic effective actions, path entropies, and the structure and meaning of thermodynamic descriptions

The meaning of thermodynamic descriptions is found in large-deviations scaling of the fluctuations probabilities. The primary large-deviations rate function is the entropy, which is the basis for both fluctuation theorems and for characterizing the thermodynamic interactions of systems. Freidlin-Wentzell theory provides a general formulation of large-deviations scaling for non-equilibrium stochastic processes, through a representation in terms of a Hamiltonian dynamical system. A number of related methods now exist to construct the Freidlin-Wentzell Hamiltonian for many kinds of stochastic processes; one method due to Doi and Peliti, appropriate to integer counting statistics, is widely used in reaction-diffusion theory. Using these tools together with a path-entropy method due to Jaynes, we show how to construct entropy functions that both express large-deviations scaling of fluctuations, and describe system-environment interactions, for discrete stochastic processes either at or away from equilibrium. A collection of variational methods familiar within quantum field theory, but less commonly applied to the Doi-Peliti construction, is used to define a "stochastic effective action", which is the large-deviations rate function for arbitrary non-equilibrium paths. We show how common principles of entropy maximization, applied to different ensembles of states or of histories, lead to different entropy functions and different sets of thermodynamic state variables. Yet the relations of among all these levels of description may be constructed explicitly and understood in terms of information conditions. The example systems considered introduce methods that may be used to systematically construct descriptions with all the features familiar from equilibrium thermodynamics, for a much wider range of systems describable by stochastic processes