We investigated the dynamics of a simple master equation describing the evolution of a probability distribution between two states, \( p_1 \) and \( p_2 \) (with \( p_1 + p_2 = 1 \)). Our focus is on the behavior of the entropy \( S \), the distance \( D \) from the uniform distribution (\( p_1 = p_2 = 1/2 \)), and the free energy \( F \). We define two ratios, \( \eta_S = \frac{dS/dt}{dF/dt} \) and \( \eta_D = \frac{dD/dt}{dF/dt} \), and find that both diverge to plus-minus infinity as the system evolves towards the uniform distribution. This divergence marks a critical transition point where the master equation temporarily loses physical meaning. However, after this divergence, the system settles into a new, well-behaved regime where the solutions stabilize at finite values, representing a new equilibrium or steady state. This two-regime behavior underscores the intricate dynamics of simple probabilistic systems as they approach and surpass equilibrium, providing insights into the complex interplay of entropy, distance, and free energy in statistical mechanics.

We study different aspects of an exactly solvable master equation (ME). Its simplicity allows one direct access to the details of its workings, highlighting significant features and peculiarities. The existence of phase transitions is unveiled.

Marek’s Disease (MD) has a significant impact on both the global poultry economy and animal welfare. The disease pathology can include neurological damage and tumour formation. Sexual dimorphism in immunity and known higher susceptibility of females to MD makes the chicken Z chromosome (GGZ) a particularly attractive target to study the chicken MD response. Previously, we used a Hy-Line F6 population from a full-sib advanced intercross line to map MD QTL regions (QTLRs) on all chicken autosomes. Here we mapped MD QTLRs on GGZ in the previously utilized F6 population with individual genotypes and phenotypes, and in eight elite commercial egg production lines with daughter-tested sires and selective DNA pooling (SDP). Four MD QTLRs were found from each analysis. Some of these QTLRs overlap regions from previous reports. All QTLRs were tested by indiviuals from the same eight lines used in the SDP and genotyped with markers located within and around the QTLRs. All QTLRs were confirmed. The results exemplify the complexity of MD resistance in chickens and the complex distribution of P-values and LD pattern and their effect on localization of the causative elements. Considering the fragments and interdigitated LD blocks while using LD to aid localization of causative elements, one must look beyond the insignificant markers, for possible distant markers and blocks in high LD with the significant block. The QTLRs found here may explain at least part of the gender differences in MD tolerance, and provide targets for mitigating the effects of MD.

In this paper we establish information theoretical bridges between 1) Thermal Heisenberg uncertainties $\Delta x \Delta p$ (at temperature $T$), and 2) LMC structural quantifiers. After having achieved such purpose, we determine to what an extent our bridges can be extended to both the semi classical and classical realms. Also, we find a strict bound relating a special LMC structural quantifier to quantum uncertainties.

We describe a 90-year-old male presenting with disequilibrium, loss of balance and difficulty walking for three days prior to initial presentation. Interestingly, he denied cough, fever or dyspnea prior to arrival. Over the course of 48 hours, the patient developed acute respiratory distress syndrome (ARDS) requiring intubation, diagnosed with COVID-19 infection and was treated in the intensive care unit where he died. Since the initial cases in Wuhan China in Dec 2019, the medical and epidemiological communities have learned much about the presenting features, symptomatology, epidemiology, transmission and common physical, laboratory and radiological findings of this disease. Although common symptoms are already established, it is very important to learn and record atypical symptoms or presentations of this highly contagious disease. By doing so, we will be able to recognize earlier atypical symptoms and prevent the environmental exposure to Health care workers and future patients as well. We report that Central disequilibrium may be such as initial presenting sign and symptom of impending respiratory failure from SARS-CoV-2 virus. These atypical findings such as presyncope may precede common respiratory complications of SARS-CoV-2.

A partial extraction procedure was used to study the distribution of uranium in the mineral phases of rocks of an aquifer of sandy-clay deposits of the Vendian in the northwest of Russia. This work is a part of a research project to develop a method for combined radiocarbon and uranium-isotope dating of groundwater. Representative aliquots of each core sample were subjected to five "partial" extractions by treatment with: distilled water, low mineralized fresh natural groundwater, minopolycarboxylic acid chelating agent (0.05M EDTA), 0.5M HCl, 15M HNO₃, and a total digestion, with U isotopes reported in this study for each procedure. The following mineral phases of core samples: adsorbed material, carbonate minerals, amorphous iron oxides, aluminosilicates partial digestion and a crystalline iron oxides, aluminosilicates total digestion and a clay/quartz resistate were characterized. Red-colored siltstones depleted in uranium in relatively readily soluble mineral phases. The concentration of adsorbed uranium was established in the amount of 15.8±2.1 - 30.5±3.9 μg/kg. Carbonate minerals contain even less of this element. In iron hydroxides and the most readily soluble aluminosilicates, its concentrations are in the range 168±24 - 212±28 μg/kg. The most insoluble fraction contains 1.65±0.21 - 4.32±0.45 mg/kg of uranium. In green-colored siltstones, the concentration of adsorbed uranium is much higher: 106±14 - 364±43 μg/kg. Carbonate minerals and amorphous iron oxides contain 1.91±0.21 - 2.34±0.26 mg/kg of uranium. In aluminosilicates and a clay/quartz resistate, uranium concentrations are 5.6±0.5 - 16.8±1.4 mg/kg. Elevated values of ²³⁴U:²³⁸U activity ratio prevail in the adsorbed material and iron hydroxides. In aluminosilicates and clay/quartz resistate, the values decrease. This indicates the replacement of primary sedimentogenic uranium by secondary hydrogenic uranium adsorbed on the surface of minerals and coprecipitated with iron hydroxides. The results obtained made it possible to carry out preliminary quantitative estimates of the retardation factor and recoil loss factor of uranium in the groundwater of siltstones of the studied Vendian aquifer.

In order to integrate genomics in breeding and development of drought tolerant groundnut genotypes, identification of genomic regions/genetic markers for drought surrogate traits is essential. We used SNP markers for a genetic analysis of the ICRISAT groundnut minicore collection for genome wide marker-trait association for some physiological traits and to determine the magnitude of linkage disequilibrium (LD) present in the genetic resources. The LD analysis showed that about 36% of loci pairs were in significant LD (P < 0.05 and r2 > 0.2) and 3.14% of the pairs were in complete LD. There was rapid decline in LD with distance and the LD was <0.2 at a distance of 41635 bp. The marker trait association (MTAs) studies revealed 20 significant MTAs (p <0.001) with 11 markers for leaf area index (4), canopy temperature (13), chlorophyll content (1) and NDVI (2). The markers explained 2 to 21% of the phenotypic variation observed. Most of the MTAs identified on the A subgenome were also identified on the respective homeologous chromosome on the B subgenome. The duplications of effect observed could be due to common ancestor of the A and B genome which explains the linkage detected between markers lying on different chromosomes seen in the current study. The present study identified a total of 20 highly significant marker trait associations with 11 markers for four physiological traits of importance in groundnut; LAI, CT, SCMR and NDVI. The markers identified in this study can serve as useful genomic resources to initiate marker-assisted selection and trait introgression of groundnut for drought tolerance. The identified markers in this study may be useful for marker assisted selection after further validation.

Characterization of genetic diversity, population structure and linkage disequilibrium is prerequisite for proper management of breeding programs and conservation of genetic resources. In this study, 186 chickpea genotypes including advanced “Kabuli” breeding lines and Iranian landrace “Desi” chickpea genotypes were genotyped using DArTseq-Based SNP markers. Out of 3339 SNPs, 1152 markers with known chromosomal position were selected for genome diversity analysis. The number of mapped SNP markers varied from 52 (LG8) to 378 (LG4), with an average of 144 SNPs per linkage group. The chromosome size that covered by SNPs varied from 16236.36 kbp (LG8) to 67923.99 kbp (LG5), while LG4 showed higher number of SNPs, with an average of 6.56 SNPs per Mbp. Polymorphism information content (PIC) value of SNP markers ranged from 0.05 to 0.50, with an average of 0.32, while the markers on LG4, LG6 and LG8 showed higher mean PIC value than average. Un-weighted Neighbor Joining cluster analysis and Bayesian-based model population structure grouped chickpea genotypes into four distinct clusters. Principal component analysis (PCoA) and Discriminant Analysis of Principal Component (DAPC) results were consistent with that of the cluster and population structure analysis. Linkage disequilibrium (LD) was extensive and LD decay in chickpea germplasm was relatively low. A few markers showed r²≥0.8, while 2961 pairs of markers showed complete LD (r²=1) and a huge LD block was observed on LG4. High genetic diversity and low kinship value between pairs of genotypes suggesting the presence of a high genetic diversity among studied chickpea genotypes. This study also demonstrated the efficiency of DArTseq-based SNP genotyping for large scale genome analysis in chickpea. The genotypic markers provided in this study are useful for various association mapping studies when combined with phenotypic data of different traits such as seed yield, abiotic and biotic stresses and therefore can be efficiently used in breeding programs to improve chickpea.

We investigate the physics of a medium-size quantum particle' gases, of the order of hundreds or thousands of fermions/bosons (far below the thermodynamic limit $N \, \rightarrow \, 10^{24}$). Appeal to microcanonical ensemble becomes then unavoidable. The so-called statistical complexity is our protagonist. Interesting facts are uncovered, both for fermions and bosons, yielded by statistical quantifiers.

This work is a generalization of the Lopez-Ruiz, Mancini and Calbet (LMC); and Shiner, Davison and Landsberg (SDL) complexity measures, considering that the state of a system or process is represented by a dynamical variable during a certain time interval. As the two complexity measures are based on the calculation of informational entropy, an equivalent information source is defined and, as time passes, the individual information associated to the measured parameter is the seed to calculate instantaneous LMC and SDL measures. To show how the methodology works, an example with economic data is presented.