Geometric and Combinatorial Aspects of NonEquilibrium Statistical Mechanics

Non-Equilibrium Statistical Mechanics is a broad subject. Grossly speaking, it deals with systems which have not yet relaxed to an equilibrium state, or else with systems which are in a steady non-equilibrium state, or with more general situations. They are characterized by external forcing and internal fluxes, resulting in a net production of entropy which quantifies dissipation and the extent by which, by the Second Law of Thermodynamics, time-reversal invariance is broken. In this thesis we discuss some of the mathematical structures involved with generic discrete-state-space non-equilibrium systems, that we depict with networks in all analogous to electrical networks. We define suitable observables and derive their linear regime relationships, we discuss a duality between external and internal observables that reverses the role of the system and of the environment, we show that network observables serve as constraints for a derivation of the minimum entropy production principle. We dwell on deep combinatorial aspects regarding linear response determinants, which are related to spanning tree polynomials in graph theory, and we give a geometrical interpretation of observables in terms of Wilson loops of a connection and gauge degrees of freedom. We specialize the formalism to continuous-time Markov chains, we give a physical interpretation for observables in terms of locally detailed balanced rates, we prove many variants of the fluctuation theorem, and show that a well-known expression for the entropy production due to Schnakenberg descends from considerations of gauge invariance, where the gauge symmetry is related to the freedom in the choice of a prior probability distribution. As an additional topic of geometrical flavor related to continuous-time Markov chains, we discuss the Fisher-Rao geometry of nonequilibrium decay modes, showing that the Fisher matrix contains information about many aspects of non-equilibrium behavior, including non-equilibrium phase transitions and superposition of modes. We establish a sort of statistical equivalence principle and discuss the behavior of the Fisher matrix under time-reversal. To conclude, we propose that geometry and combinatorics might greatly increase our understanding of nonequilibrium phenomena.

Molecular basis of Osteoarthritis and aspects of cellular senescence in disease

The aim of this study is to investigate on some molecular mechanisms contributing to the pathogenesis of osteoarthritis (OA) and in particular to the senescence of articular chondrocytes. It is focused on understanding molecular events downstream GSK3β inactivation or dependent on the activity of IKKα, a kinase that does not belong to the phenotype of healthy articular chondrocytes. Moreover, the potential of some nutraceuticals on scavenging ROS thus reducing oxidative stress, DNA damage, and chondrocyte senescence has been evaluated in vitro. The in vitro LiCl-mediated GSK3β inactivation resulted in increased mitochondrial ROS production, that impacted on cellular proliferation, with S-phase transient arrest, increased SA-β gal and PAS staining, cell size and granularity. ROS are also responsible for the of increased expression of two major oxidative lesions, i.e. 1) double strand breaks, tagged by γH2AX, that associates with activation of GADD45β and p21, and 2) 8-oxo-dG adducts, that associate with increased IKKα and MMP-10 expression. The pattern observed in vitro was confirmed on cartilage from OA patients. IKKa dramatically affects the intensity of the DNA damage response induced by oxidative stress (H2O2 exposure) in chondrocytes, as evidenced by silencing strategies. At early time point an higher percentage of γH2AX positive cells and more foci in IKKa-KD cells are observed, but IKKa KD cells proved to almost completely recover after 24 hours respect to their controls. Telomere attrition is also reduced in IKKaKD. Finally MSH6 and MLH1 genes are up-regulated in IKKαKD cells but not in control cells. Hydroxytyrosol and Spermidine have a great ROS scavenging capacity in vitro. Both treatments revert the H2O2 dependent increase of cell death and γH2AX-foci formation and senescence, suggesting the ability of increasing cell homeostasis. These data indicate that nutraceuticals represent a great challenge in OA management, for both therapeutical and preventive purposes.

Comparison of Experimental and Theoretical Structures of a Transition State Analogue Used for the Induction of Anti-Cocaine Catalytic Antibodies

Comparison of the crystal structure of a transition state analogue that was used to raise catalytic antibodies for the benzoyl ester hydrolysis of cocaine with structures calculated by ab initio, semiempirical, and solvation semiempirical methods reveals that modeling of solvation is crucial for replicating the crystal structure geometry. Both SM3 and SM2 calculations, starting from the crystal structure TSA I, converged on structures similar to the crystal structure. The 3-21G(*)/HF, 6-31G*/HF, PM3, and AM1 calculations converged on structures similar to each other, but these gas-phase structures were significantly extended relative to the condensed phase structures. Two transition states for the hydrolysis of the benzoyl ester of cocaine were located with the SM3 method. The gas phase calculations failed to locate reasonable transition state structures for this reaction. These results imply that accurate modeling of the potential energy surfaces for the hydrolysis of cocaine requires solvation methods.

A Simple Visual Demonstration of Phase Diagram Concepts for an Introductory Materials Science Course Using Colored Solvents

A simple and effective demonstration to help students comprehend phase diagrams and understand phase equilibria and transformations is created using common chemical solvents available in the laboratory. Common misconceptions surrounding phase diagram operations, such as components versus phases, reversibility of phase transformations, and the lever rule are addressed. Three different binary liquid mixtures of varying compatibility create contrastive phase equilibrium cases, where colorful dyes selectively dissolved in each of corresponding phases allow for quick and unambiguous perceptions of solubility limit and phase transformations. Direct feedback and test scores from a group of students show evidence of the effectiveness of the visual and active teaching tool.

Poverty in Slovenia: A Conseqence of Economic Transition

Slovenia is considered to be one of the most successful Central and Eastern European countries undergoing the process of transition. It has a high GDP per capita (the highest in the Visegrad group) amounting to about 7200 US dollars (at the exchange rates pertaining during Ms. Stropnik's research). In 1994, a low rate of inflation, a low level of public debt and almost balanced public finances, were all positive elements. However, there is a darker side, for instance the dramatic increase in unemployment and (somewhat less dramatic) fall in production during the transition period. This analysis aimed to provide insights into what is actually happening at the household level, since households are the ultimate bearers of macroeconomic and social change. The final output totalled 166 pages in English and Slovenian, available also on disc. The income concept used by Ms. Stropnik is that of the disposable (monetary) household income, i.e. the cash income of all household members - including social security transfers and family benefits, and the net sum of taxes and social security contributions - plus the equivalent of domestic production, used in the household. Non-monetary income sources, such as household own production, benefits in kind, subsidies for goods and services, and fringe benefits, were not taken into account. The concept of relative and objective poverty was followed. Poverty means having less than others in society, it is a state of relative deprivation. Objective aspects of the situation, e.g. command over resources (i.e. the household income) and the relative position of the household in the income distribution, determine who is poor and who is not. Changes in household composition - an increase in the number of pensioners, unemployed and self-employed, concomitant with a large decrease in the number of employees - obviously played a part in the changing structure of household income sources during this period. The overall decrease in the share of wages and salaries from primary employment in 1993 is to be observed in all income deciles. On the other hand, the importance of salaries gained from secondary employment has increased in all deciles. The lower seven deciles experienced a sharp rise in the share of social benefits in the period 1988-1993, mostly because of the increase in the number of persons entitled to claim unemployment benefits. In Slovenia, income inequality has increased considerably during the 1988-1993 period. To make matters worse, the large increase in income inequality occurred in a period of falling real incomes. In 1983 the bottom decile disposed of 3.8 percent and the top decile disposed of 23.4 percent of total monetary income in Slovenia, whereas by 1993 the same statistics revealed 3.1 percent and 18.9 percent respectively. Unemployment greatly increases the risk of living in poverty. In 1993, 35 per cent of all unemployed persons in Slovenia were living in the lowest income quintile. Ms. Stropnik found certain features that were specific to Slovenia and not shared by most countries in transition. For example, the relative income position of pensioners has improved. Retirement did not increase the risk of poverty in 1993 as much as it did in 1983 and 1988. Also, it appears that children have not been particularly hard-hit by the transition upheavals. The incidence of poverty amongst children has not increased in the period 1983-1993. Children were also fairly evenly distributed across income quintiles. In 1983, 11.8 percent of households with children aged 18 or less were poor. In 1993, this figure was 8.4 per cent. On the other hand, poor households with children were, in comparison with other households of the same type, poorer in 1993 than in 1983. Ms. Stropnik also analysed the impact of social transfers. Her conclusion was that the level of social transfers prevented them from being successful in alleviating poverty. Family policy transfers (child allowances, child tax allowances, subsidised child care) did, however, contribute to the lowering of income inequality between families with and without children, and amongst families with different numbers of children. Ms. Stropnik is determined that the results of her research be used in the creation of social policy aimed at helping the poor. She quotes Piachaud approvingly: "If the term 'poverty' carries with it the implication and moral imperative that something should be done about it, then the study of poverty is only ultimately justifiable if it influences individual and social attitudes and actions."

Structural aspects of postnatal lung development - alveolar formation and growth

The human lung is born with a fraction of the adult complement of alveoli. The postnatal stages of human lung development comprise an alveolar stage, a stage of microvascular maturation, and very likely a stage of late alveolarization. The characteristic structural features of the alveolar stage are well known; they are very alike in human and rat lungs. The bases for alveolar formation are represented by immature inter-airspace walls with two capillary layers with a central sheet of connective tissue. Interalveolar septa are formed by folding up of one of the two capillary layers. In the alveolar stage, alveolar formation occurs rapidly and is typically very conspicuous in both species; it has therefore been termed 'bulk alveolarization'. During and after alveolarization the septa with double capillary networks are restructured to the mature form with a single network. This happens in the stage of microvascular maturation. After these steps the lung proceeds to a phase of growth during which capillary growth by intussusception plays an important role in supporting gas exchange. In view of reports that alveoli are added after the stage of microvascular maturation, the question arises whether the present concept of alveolar formation needs revision. On the basis of morphological and experimental findings we can state that mature lungs contain all the features needed for 'late alveolarization' by the classical septation process. Because of the high plasticity of the lung tissues, late alveolarization or some forms of compensatory alveolar formation may be considered for the human lung.

High-temperature induced dehydration, phase transition and exsolution in amicite: A single-crystal X-ray study

Temperature dependent single-crystal X-ray data were collected on amicite K4Na4(Al8Si8O32)·11H2O from Kola Peninsula (Russia) in steps of 25 °C from room temperature to 175 °C and of 50 °C up to 425 °C. At room temperature amicite has space group I2 with a = 10.2112(1), b = 10.4154(1), c = 9.8802(1) Å, β = 88.458(1)°, V = 1050.416(18) Å3. Its crystal structure is based on a Si–Al ordered tetrahedral framework of the GIS type with two systems of eight-membered channels running along the a and c axes. Extraframework K and Na cations are ordered at two fully occupied sites. Above 75 °C amicite was found to partly dehydrate into two separate but coherently intergrown phases, both of space group I2/a, one K-rich ∼K8(Al8Si8O32) ·4H2O (at 75 °C: a = 10.038(2), b = 9.6805(19), c = 9.843(2) Å, β = 89.93(3)°, V = 956.5(3) Å3) and the other Na-rich ∼Na8(Al8Si8O32)·2H2O (at 75 °C: a = 9.759(2), b = 8.9078(18), c = 9.5270(19) Å, β = 89.98(3)°, V = 828.2(3) Å3). Upon further heating above 75 °C the Na- and K-phases lost remaining H2O with only minor influence on the framework structure and became anhydrous at 175 °C and 375 °C, respectively. The two anhydrous phases persisted up to 425 °C. Backscattered electron images of a heated crystal displayed lamellar intergrowth of the K- and Na-rich phases. Exposed to ambient humid conditions K- and Na-rich phases rehydrated and conjoined to the original one phase I2 structure.

High-Pressure Behavior and Phase Stability of Al5BO9, a Mullite-Type Ceramic Material

Phase stability, elastic behavior, and pressure-induced structural evolution of synthetic boron-mullite Al5BO9 (a = 5.6780(7), b = 15.035(6), and c =7.698(3) Å, space group Cmc21, Z = 4) were investigated up to 25.6(1) GPa by in situ single-crystal synchrotron X-ray diffraction with a diamond anvil cell (DAC) under hydrostatic conditions. No evidence of phase transition was observed up to 21.7(1) GPa. At 25.6(1) GPa, the refined unit-cell parameters deviated significantly from the compressional trend, and the diffraction peaks appeared broader than at lower pressure. At 26.7(1) GPa, the diffraction pattern was not indexable, suggesting amorphization of the material or a phase transition to a high-pressure polymorph. Fitting the P–V data up to 21.7(1) GPa with a second-order Birch–Murnaghan Equation-of-State, we obtained a bulk modulus KT0 = 164(1) GPa. The axial compressibilities, here described as linearized bulk moduli, are as follows: KT0(a) = 244(9), KT0(b) = 120(4), and KT0(c) = 166(11) GPa (KT0(a):KT0(b):KT0(c) = 2.03:1:1.38). The structure refinements allowed a description of the main deformation mechanisms in response to the applied pressure. The stiffer crystallographic direction appears to be controlled by the infinite chains of edge-sharing octahedra running along [100], making the structure less compressible along the a-axis than along the b- and c-axis.

How do different aspects of self-regulation predict successful adaptation to school?

Self-regulation plays an important role in successful adaptation to preschool and school contexts as well as in later academic achievement. The current study relates different aspects of self-regulation such as temperamental effortful control and executive functions (updating, inhibition, and shifting) to different aspects of adaptation to school such as learning-related behavior, school grades, and performance in standardized achievement tests. The relationship between executive functions/effortful control and academic achievement has been established in previous studies; however, little is known about their unique contributions to different aspects of adaptation to school and the interplay of these factors in young school children. Results of a 1-year longitudinal study (N = 459) revealed that unique contributions of effortful control (parental report) to school grades were fully mediated by children’s learning-related behavior. On the other hand, the unique contributions of executive functions (performance on tasks) to school grades were only partially mediated by children’s learning-related behavior. Moreover, executive functions predicted performance in standardized achievement tests exclusively, with comparable predictive power for mathematical and reading/writing skills. Controlling for fluid intelligence did not change the pattern of prediction substantially, and fluid intelligence did not explain any variance above that of the two included aspects of self-regulation. Although effortful control and executive functions were not significantly related to each other, both aspects of self-regulation were shown to be important for fostering early learning and good classroom adjustment in children around transition to school.

First order thermal phase transition with 126 GeV Higgs mass

We study the strength of the electroweak phase transition in models with two light Higgs doublets and a light SU(3)c triplet by means of lattice simulations in a dimensionally reduced effective theory. In the parameter region considered the transition on the lattice is significantly stronger than indicated by a 2-loop perturbative analysis. Within some ultraviolet uncertainties, the finding applies to MSSM with a Higgs mass mh ≈ 126 GeV and shows that the parameter region useful for electroweak baryogenesis is enlarged. In particular (even though only dedicated analyses can quantify the issue), the tension between LHC constraints after the 7 TeV and 8 TeV runs and frameworks where the electroweak phase transition is driven by light stops, seems to be relaxed.

Molecular and pathogenetic aspects of tumor budding in colorectal cancer.

In recent years, tumor budding in colorectal cancer has gained much attention as an indicator of lymph node metastasis, distant metastatic disease, local recurrence, worse overall and disease-free survival, and as an independent prognostic factor. Tumor buds, defined as the presence of single tumor cells or small clusters of up to five tumor cells at the peritumoral invasive front (peritumoral buds) or within the main tumor body (intratumoral buds), are thought to represent the morphological correlate of cancer cells having undergone epithelial-mesenchymal transition (EMT), an important mechanism for the progression of epithelial cancers. In contrast to their undisputed prognostic power and potential to influence clinical management, our current understanding of the biological background of tumor buds is less established. Most studies examining tumor buds have attempted to recapitulate findings of mechanistic EMT studies using immunohistochemical markers. The aim of this review is to provide a comprehensive summary of studies examining protein expression profiles of tumor buds and to illustrate the molecular pathways and crosstalk involved in their formation and maintenance.

Computer simulation of electrophoretic aspects of enantiomer migration and separation in capillary electrochromatography with a neutral selector.

A computer simulation study describing the electrophoretic separation and migration of methadone enantiomers in presence of free and immobilized (2-hydroxypropyl)-β-CD is presented. The 1:1 interaction of methadone with the neutral CD was simulated by using experimentally determined mobilities and complexation constants for the complexes in a low-pH BGE comprising phosphoric acid and KOH. The use of complex mobilities represents free solution conditions with the chiral selector being a buffer additive, whereas complex mobilities set to zero provide data that mimic migration and separation with the chiral selector being immobilized, that is CEC conditions in absence of unspecific interaction between analytes and the chiral stationary phase. Simulation data reveal that separations are quicker, electrophoretic displacement rates are reduced, and sensitivity is enhanced in CEC with on-column detection in comparison to free solution conditions. Simulation is used to study electrophoretic analyte behavior at the interface between sample and the CEC column with the chiral selector (analyte stacking) and at the rear end when analytes leave the environment with complexation (analyte destacking). The latter aspect is relevant for off-column analyte detection in CEC and is described here for the first time via the dynamics of migrating analyte zones. Simulation provides insight into means to counteract analyte dilution at the column end via use of a BGE with higher conductivity. Furthermore, the impact of EOF on analyte migration, separation, and detection for configurations with the selector zone being displaced or remaining immobilized under buffer flow is simulated. In all cases, the data reveal that detection should occur within or immediately after the selector zone.