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The marginalization of the hijra identity in postcolonial Pakistan perpetuates the inequalities that have dogged the transgender community since the colonial era. Although Pakistan has since ratified all concerned UN treaties aimed at protecting transgender people and preventing human rights violations against them, the country’s gender-variant population nevertheless remains vulnerable to these transgressions. As such, this study aims to explore the following inquiry: “What are the lifeways of the hijra community and how do hijra people face human rights violations in their daily life activities?”
The identity construction of the hijra is a complex process. Pakistan is a patriarchal society that determines gender based on biological sex. While a genitally ambiguous child is generally recognized as intersexed, the family usually obscures this circumstance or tries to enforce a predominantly male identity onto the child. To some degree, an intersexed child is allowed to perform feminine roles, particularly when compared to a biologically male individual who is inclined toward femininity. They may partake in “girls’ games” or in “women’s chores” like cooking; they may opt to don feminine clothing and jewelry or practice walking and talking “like a girl.” Many family members and relatives consider such actions a threat to family honor and/or an indication of weakness, which in turn renders the child vulnerable to sexual or physical assault. Abuse also causes some gender-variant children to drop out of school. As adults, many hijras do not see childhood sexual encounters as assault, particularly because they considered themselves to be feminine even from a young age. Nevertheless, experiences of isolation, abuse, and exclusion often compel a gender-variant child to seek company outside of his/her family of orientation.
Many transgender individuals see redemption in joining the hijra community: there, a new identity is defined and shaped. New members mirror themselves after more senior hijras. In the community, relationships are solidified through similar childhood experiences and interests as well as a shared freedom to express the outer reflection of an “inner feminine soul.” Here, they accept the childhood label affixed to them by heteronormative society: hijra. In fact, the identity now becomes the key to economic viability and socialization.
The predominant livelihood strategies within the hijra community are dancing and prostitution. New members must adhere to stringent norms and rules; they risk (sometimes severe) punishment if they do not. For example, a new hijra must adopt a very strict feminine appearance; if she does not appear feminine enough she may be socially isolated or physically punished. Similarly, a hijra is required to remain passive during sex. In fact, because hijras are stereotyped as passive and vulnerable, many clients physically exploit or even rape them. If she tries to resist, a hijra may face physical violence and, in extreme circumstances, death. Reporting abuse to law enforcement authorities often leads to further exploitation. As such, whether dancing or performing sexually, hijras are encouraged to do whatever is asked of them.
In the last decade, the Supreme Court of Pakistan has taken significant steps to ensure the rights of transgender people. The Court has similarly compelled local governments to amend existing legislation in order to protect the transgender community. Nevertheless, discrepancies exist in legislative and judicial interpretations of the transgender identity, which continues to impede the struggle for basic rights. Indeed, there is a long way to go in the effort to incorporate transgender people into the folds of mainstream Pakistani society.
In this work we provided additional insights into our understanding of bulk QCD matter through the study of the transport coeffcients which govern the non-equilibrium microscopical processes of statistical ensembles. Specically, we focused on the low energy regime corresponding to the hadron gas, as the properties of this region of the phase diagram are still relatively unknown, and existing calculations for the transport coeffcients are either scarce, contradictory, or somewhat limited in scope; this thesis' main goal was thus to shed some light on this by providing new independent calculations of these quantities.
We subsequently presented two formalisms which can be used to calculate transport coeffcients. The first one (which also was the main tool we used in the following chapters to produce our results) relies on the development of so-called Green-Kubo formulas, which relate non-equilibrium dissipative fluctuations with transport coeffcients; notably, the off-diagonal components of the energy-momentum tensor are shown to be related to the shear viscosity, its diagonal components to the bulk viscosity and fluctuations in the electric current can be related to the electric conductivity. We additionally introduced two new conductivities, namely the baryon-electric and strange electric conductivities, which we dubbed, together with the already known electric one, the "cross-conductivity", which encodes information about how electric fluctuations are correlated to changes in electric, baryonic or strange currents, or vice-versa. The second way of calculating transport coeffcient which we discussed consists in linearizing the collision term of the Boltzmann equation through the Chapman-Enskog formalism. While in principle providing direct semi-analytical results for the transport coeffcients, this approach is complicated to implement when more than a few species are considered, and as such was then mostly used as a tool to calibrate our Green-Kubo calculations.
The hadron gas model that we used for all calculations, namely the transport approach SMASH, was then presented. The main features of the model were explained, such as the collision criterion, the considered degrees of freedom and the specific way in which they microscopically interact with each other. It was verified that SMASH does reproduce analytical results of the Boltzmann equation in an expanding universe scenario, thus showing the equivalence of this transport approach and the associated kinetic theory results. A special care was taken to detail the ways in which a state of thermal and chemical equilibrium (which is necessary for Green-Kubo relations to be valid) can be reached and described using SMASH.
...
Transport mechanism of a multidrug resistance protein investigated by pulsed EPR spectroscopy
(2019)
In human several diseases result from malfunctions of ATP-binding cassette (ABC) systems, which form one of the largest transport system superfamily. Many ABC exporters contain asymmetric nucleotide-binding sites (NBSs) and some of them are inhibited by the transported substrate.1 For the active transport of diverse chemically substrates across biological membranes, ABC transport complexes use the energy of ATP binding and subsequent hydrolysis. In this thesis, the heterodimeric ABC exporter TmrAB2,3 from Thermus thermophilus, a functional homolog of the human antigen translocation complex TAP, was investigated by using pulsed electron-electron double resonance (PELDOR/DEER) spectroscopy. In the presence of ATP, TmrAB exists in an equilibrium between inward- and outward-facing conformations. This equilibrium can be modulated by changing the ATP concentration, showing asymmetric behaviour in the open-to-close equilibrium between the consensus and the degenerate NBSs. At the degenerate NBS the closed conformation is more preferred and closure of one of the NBSs is sufficient to open the periplasmic gate at the transmembrane domain (TMD).3 By determining the temperature dependence of this conformational equilibrium, the thermodynamics of the energy coupling during ATP-induced conformational changes in TmrAB were investigated. The results demonstrate that ATP-binding alone drives the global conformational switching to the outward-facing state and allows the determination of the entropy and enthalpy changes for this step. With this knowledge, the Gibbs free energy of this ATP induced transition was calculated. Furthermore, an excess of substrate, meaning trans-inhibition of the transporter is resulting mechanistically in a reverse transition from the outward-facing state to an occluded conformation predominantly.3 This work unravels the central role of the reversible conformational equilibrium in the function and regulation of an ABC exporter. For the first time it is shown that the conformational thermodynamics of a large membrane protein complex can be investigated. The presented experiments give new possibilities to investigate other related medically important transporters with asymmetric NBSs or other similar protein complexes.
Protein quality control (PQC) machinery is in charge of ensuring protein homeostasis in the cell, i.e. proteostasis. Chaperones assist polypeptides throughout their maturation until functionality is achieved. This process might be disrupted in the presence of mutations or external damaging agents that affect the folding and stability of proteins. In this case, proteins can be efficiently recognized and targeted for degradation in a controlled manner. Ubiquitylation refers to the covalent attachment of one or more ubiquitin moieties to faulty proteins, thus triggering their degradation by the 26S proteasome.
More than 30% of proteins need cofactor molecules. Lack of cofactors renders proteins non-functional. We wanted to understand how the PQC deals with wild-type proteins in the absence of their cofactors. Several studies have indicated the importance of the riboflavin-derived cofactor FAD in the stability of individual flavoproteins, and hence we assumed that loss of flavin should mediate a targeted degradation of this group of proteins. Indeed, our mass spectrometry experiments showed that flavoproteome levels decreased under riboflavin starvation. The oxidoreductase NQO1 was used as a model enzyme to further investigate the mechanism of flavoproteome targeting by the PQC. We showed that cofactor loading determines ubiquitylation of NQO1 by the co-chaperone CHIP, both in vivo and in vitro. Furthermore, subtle changes in the C-terminus of NQO1 in the absence of FAD seemed to be crucial for this recognition event. ApoNQO1 interactome differed from holoNQO1. Chaperones and degradation factors were enriched on NQO1 upon cofactor withdrawal, probably to support maturation and prevent aggregation of the enzyme.
Loss of protein folding and stability, even to a small extent, can enhance the aggregating behavior of proteins. Proper loading with FAD reduced the co-aggregation of NQO1 with Aβ1-42 peptide. We assumed that the flavoproteome might represent aggregating-prone species under riboflavin deprivation. Supportingly, reversible apoNQO1 aggregates were observed in vivo in the absence of cofactor. General amyloidogenesis in vivo also increased under these conditions, apparently as a result of flavoproteome destabilization. In this context, we think that our data might have important implications considering the onset and development of conformational diseases.
This work has shed some light on the therapeutic implications of riboflavin deficiency as well. The sensitivity of melanoma cells towards the alkylating agent methyl methanesulfonate (MMS) increased under riboflavin starvation. Subsequent analyses indicated that a complex metabolic reorganization, mostly affecting proliferation and energy metabolism, occurs in response to starvation. What we suggest to call “flavoaddiction” can be understood as the dependence of melanoma cells on the flavoproteome structural and functional intactness to survive chemotherapy. Understanding this cellular reprogramming in detail might reveal new possibilities for future therapies.
Uncaging approach, native membrane dynamics and lipidic cubic phases in biomolecular solid-state NMR
(2019)
It was previously shown for the Escherichia coli diacylglycerol kinase (DgkA) that enzyme-reactions at the membrane interface can be monitored by solid-state NMR. However, such studies can face problems due to limited accessibility of the active sites: Natural substrates for membrane enzymes, but also ligands for membrane proteins or lipid mediators, are either partitioning into the membrane and cannot be added easily, or if soluble exhibit accessibility restrictions, as they cannot freely pass through lipid bilayers. This situation complicates quantitative kinetic analysis of biochemical processes such as enzyme activity, ligand binding, but also oligomerization or folding reactions in the membrane or at its interface under MAS NMR conditions.
To overcome these limitations the feasibility and possible advantages of the uncaging approach as a new tool for biomolecular solid-state NMR to trigger reactions by light have been explored. DgkA’s enzymatic activity, exemplary of a biochemical process on the membrane interface, was thereby triggered in situ during MAS by light-induced release of its substrates that were rendered inactive with photolabile protecting groups. To be capable of uncaging sufficient amounts of substrate during MAS to follow the enzymatic reaction via 31P real-time NMR measurements, several illumination variants including an existing illumination setup to study retinal proteins under cryogenic conditions via DNP enhanced NMR were tested. As uncaging of micromole amounts of substrates requires a higher flux compared to initiation of a photocycle in retinal proteins, a new illumination setup was built with Bruker Biospin and Leoni Fibertech. It consists of a modified MAS probe and a suitable fiber bundle, allowing to efficiently couple light from high power LEDs into a sapphire rotor containing the sample, without disturbing the magnetic field homogeneity or sample rotation. By reducing the sample volume to the illuminated area up to 60 mM ATP were released by uncaging NPE ATP to initiate DgkA’s activity in several tested membrane mimetics. These mimetics included liposomes and bicelles, which are well established in the field of biomolecular solid state NMR as well as the optically transparent lipidic cubic phase of monoolein, widely used in membrane protein crystallography, but not yet well characterized as membrane mimetic under MAS conditions. A unique and powerful but compared to time and spatial resolution often underrepresented advantage of the uncaging approach for biophysical studies has been demonstrated by successful uncaging of a non-miscible lipid substrate to trigger DgkA’s kinase reaction: Initiation of processes that cannot easily be triggered by mixing. Examples of these are reactions involving highly hydrophobic, membrane partitioning compounds including lipid substrates, ligands or interaction partners, but also oligomerization or folding of biomacromolecules. The herein performed experiments therefore serve as a first demonstration of the uncaging approach’s feasibility and compatibility with a wide variety of membrane mimetics and give a first indication of its potential for a variety of biomolecular solid state NMR experiments.
As high accessibility for solutes has been a second focus for the choice of membrane mimetics, DgkA’s activity in the lipidic cubic phases of monoacylglycerols with its two continuous networks of water channels has been further characterized. Kinetic parameters obtained from 31P real time solid state NMR experiments revealed that DgkA’s activity is similar to activities obtained in swollen cubic phases in a bath solution with wider water channels. Diffusion of ATP in a non swollen cubic phase was however strongly reduced compared to ATP in solution as diffusion measurements showed. Therefore, saturation of the enzyme required distinctly higher ATP concentrations. These results thereby underline the advantage of a non invasive and label free method like NMR to directly gain information about enzymatic reactions of immobilized enzymes in porous materials. The obtained wealth of information from 31P real time NMR experiments and biochemical assays in different membrane mimetics in presence and absence of lipid substrates and activators also provided further insight into DgkA’s enzymatic activity. It confirms ATP binding and hydrolysis in the absence of a lipid substrate, in agreement with the proposed mode of substrate binding, and allowed to estimate the in vivo relevance of previously observed ATPase activity in liposomes.
Further exploration of the cubic phase as membrane mimetic for protein solid state NMR revealed its high stability under MAS at elevated temperatures and capacity to reconstitute sufficient amounts of DgkA. Unlike monoolein, DgkA was cross-polarizable in a cubic phase and exhibited similar dynamics compared to DgkA reconstituted into liposomes, allowing to acquire the herein shown dipolar coupling based 2D protein spectra. As lipidic cubic phases are not containing phospholipids, monoacylglycerols could be especially useful as membrane mimetics for 31P correlation spectra. Initial experiments under DNP conditions, where in liposomes line broadening causes severe overlap of phospholipid signals and unspecific cross polarization highlight this aspect.
In summary, herein reported results of the experiments performed with lipidic cubic phases demonstrate that they are robust and versatile membrane mimetics. They could be of advantage for a variety of solid-state NMR experiments where either optical transparency for efficient illumination is desired, accessibility for solutes and membrane components under MAS is required, or interference of phosphorous signals of other membrane mimetics must be avoided.
In the second chapter of this thesis 1H solid-state NMR as a label free method to probe membrane order and dynamics directly within a cellular and disease relevant context was used to observe the effects of soluble epoxide hydrolase (sEH) encoding gene knock-outs on membrane dynamics. Knock-out of the sEH encoding gene changed the overall membrane dynamics in the physiological temperature range of native membranes derived from mouse brains, making the bulk membrane more dynamic. To confirm that these effects are related to the enzymatic activity of sEH, substrates and products of sEH were added to evaluate their effects on membrane dynamics. 19,20 dihydroxydocosapentaenoic acid (DHDP), a product of sEH, partially reversed the knock out phenotype in a concentration dependent manner whereas the substrate 19,20 epoxydocosapentaenoic acid did not cause any effects. As both polyunsaturated fatty acids did not show differences in phase behavior in a simple phospholipid bilayer these results provide evidence that the previously observed concentration dependent DHDP induced relocation of cholesterol away from detergent resistant lipid raft fractions is associated with alteration of membrane dynamics. Therefore, also the effect of cholesterol removal via cyclodextrin on membrane dynamics was analyzed. Removal of cholesterol led to a similar temperature profile of wild type and knock out membranes thereby supporting the hypothesis that DHDP induced relocation of cholesterol is causing altered membrane dynamics. These alterations have been shown by the lead authors of the collaborative research project to induce relocation of various membrane proteins and are involved in the development of diabetic retinopathy. Furthermore, in this context inhibition of sEH has been shown to inhibit diabetic retinopathy and proposed as target for prevention of one of the leading causes of blindness in the developed world.
To gain a better understanding of complex mechanisms in biological systems, simultaneous control over multiple processes is key. To this purpose selective photouncaging has been developed. Photo-uncaging is an experimental scheme in which a molecule of interest has been inactivated synthetically and is activated by light. Usually a bond is cleaved and a leaving group is set free. The molecule which inactivates the molecule of interest and sets the leaving group free is called (photo-)cage. In a selective photo-uncaging scheme a number of leaving groups can be released independently, usually by irradiation with light of different wavelengths. This approach is, however, seriously limited in its applicability due to the properties of the involved cages and irradiation schemes. A major drawback is the usually quite broad UV-Vis absorption of the cages. This makes a selective activation by light difficult and limits the maximal number of independent cages severely.
Therefore, the aim of this thesis is to introduce the Vibrationally Promoted Electronic Resonance (VIPER) 2D-IR pulse sequence in a alternative selective uncaging scheme.
The VIPER 2D-IR pulse sequence is a spectroscopic tool which allows to generate 2D-IR signals whose lifetime are independent of the vibrational relaxation lifetime. It has been first used to monitor chemical exchange. It consists of a narrowband infared pump pulse, a subsequent UV-Vis pump pulse and a broadband infrared probe pulse. The UV-Vis pump pulse is off-resonant with regard to the UV-Vis absorption band. Electronic excitation becomes only possible, if the infrared pump pulse modulates the UV-Vis transition of the IR-excited molecule. This modulation brings the UV-Vis transition in resonance with the UV-Vis pump pulse. Thereby, only the molecules which were pre-excited with the infrared pulse can be excited into the electronically excited state. A computational prediction of the modulation was carried out by Jan von Cosel in the Burghardt group.
The narrowband infrared pump pulse can be used to selectively excite a subensemble of molecules in a mixture into an electronically excited state even if the UV-Vis spectra of all molecules are virtually identical. For this the sub-ensemble needs to exhibit an identifiable infrared spectrum. Combined with the introduction of isotope labels, which lead to changes in the infrared absorption spectra, the larger selectivity in the infrared region can be exploited for an alternative selective uncaging approach. In VIPER uncaging the infrared pump pulse selects the species and the subsequent UV-Vis pulse provides the energy needed for electronic excitation upon which the photo cleavage can occur.
After an introduction of the principle idea of uncaging and VIPER spectroscopy, the concept of VIPER uncaging is introduced and its limits and requirements are discussed. Some examples for possible VIPER cages are reviewed.
A coumarin molecule (7-diethylamino coumarin) which can release an azide group was chosen as a first test molecule for VIPER uncaging. Its isotopomers were characterized to determine suitable spectroscopic markers for successful uncaging and to find fitting experimental conditions. The chosen coumarin cage has an UV-Vis absorption band at approximately 380 nm and a steep flank on the high wavelength side of the band. The quantum yield for the azide compound is between 10-20 % depending on the solvent’s water content. The release was found to be on a picosecond timescale which is among the fastest known photo reactions, but the photo reaction mechanism has proven to be not straightforward. For the VIPER experiment on the mixture two isotopomers were chosen with a 13C atom at different positions. In one species a ring mode of the coumarin is changed by the 13C atom. In the other isotopomer the carbonyl stretching mode is influenced. The change in the ring mode region allows to select one species or the other with the infrared pre-excitation. Because of experimental difficulties only isotopomers with the same leaving group could be used. The successful selective electronic excitation of the individual isotopomers in a mixture was monitored by probing the carbonyl region.
As a second VIPER cage, para-hydroxyphenacyl (pHP) was chosen. A thiocyanate group was selected as leaving group. pHP cages have their electronic transition in the UV, with a maximum absorption at 290 nm. The shape of the spectrum is suitable and the quantum yield is very high, with values in the literature of up to 90 %. Also the photo reaction is well studied and the expected byproducts are well characterized. The chosen isotopologues were characterized spectroscopically. The resulting data on the photo reaction were in agreement with the mechanism proposed in the literature. The mixture for the VIPER experiment consisted of two isotopologues, where for one species all the C atoms in the ring were labelled and for the other the C-atom in the thiocyanate leaving group was labelled. Here the release of the different leaving groups, labelled and unlabelled thiocyanate, could be monitored selectively. This shows that it is possible to selectively release a molecule in a mixture of caged molecules by applying the VIPER pulse sequence.
The samples were synthesized by Matiss Reinfelds from the Heckel group and the VIPER experiments were done together with Carsten Neumann and with support
of the Bredenbeck group.
The leaving groups were chosen because of their infrared absorption which allowed to directly monitor the successful cleavage by spectroscopy. This was needed for the proof-of-concept experiment and to allow direct optimization of the experimental parameters but is not necessarily a requirement for VIPER uncaging.
Concerning the selectivity of the VIPER uncaging, the approach is at the moment mainly limited by the infrared pulse energy. The selective VIPER excitation is competing with unselective excitation directly by just the UV-Vis pulse. A more intense infrared pump pulse would increase only the selective VIPER excitation and thereby improve the contrast to the unspecific background.
To address this issue, the first steps towards an alternative infrared light generation are undertaken. In this alternative approach the infrared light for preexcitation is directly generated by difference frequency generation of the laser output, i.e. the high energy 800 nm fundamental, and the output of a non-collinear optical parametric amplifier (NOPA). To achieve a narrowband pump pulse the pulses are chirped before mixing. In the scope of this thesis a NOPA has been installed and the mixing has been tested with available test crystal medium. While infrared wavelength region and power were not in the aspired range with this alternative crystal the feasibility of mixing between a NOPA output and the fundamental could be shown.
Other possibilities to increase the contrast to the unspecific background excitation by the UV-Vis pump pulse are discussed. For most applications of selective VIPER uncaging the detection by fs-laser spectroscopy will not be needed and could be replaced by other methods e.g. chromatography. This will allow the experimental parameters of the VIPER pulse sequence to be changed in a way which reduces unspecific excitation i.e. reducing the UV-Vis-pump energy and result in much better contrast.
In conclusion, the experimental data in this thesis shows the VIPER pulse sequence to be applicable to selective uncaging schemes and indicates measures to arrive at the specificity necessary for uncaging applications. This thesis was focused on uncaging photo reactions with isotopomers and isotopologues, but other types of photo reactions could in principle be controlled in the same way. It should be possible to address different isomers in mixtures or different ground states of proteins selectively. The discussed experiments are a significant step towards control over photo reactions in mixtures.
Recently, carbonates have attracted a lot of attention, due to the recognition of their importance in the global carbon cycle. This was enabled by improvement of the experimental techniques that allow for investigating the stability, structure, and physical properties of materials and high-pressures and high-temperatures, that is, they allow for investigating minerals and geochemical processes at the conditions occurring deep inside Earth. Although a lot of research has been focused on carbonates, there are still some open questions regarding their structure and physical properties at such extreme conditions. The aim of this thesis is to establish a deeper understanding of the nature of the phase transitions in carbonates by studying how do the atoms building up the crystal structure vibrate, that is lattice dynamics. The methodology adapted in this study is a combination of experimental and computational methods which allows for a very thorough examination of the problem. The computational approach allows to determine parameters that are elusive or tedious to measure, and the experimental results provide a solid benchmark for the calculations. This tandem of methods has been widely used for investigating lattice dynamics of various materials. In this study it was used to elucidate the structure and properties of carbonates in the deep Earth conditions
Variation in enclitic possessive constructions in Southern Italian dialects: a syntactic analysis
(2019)
This thesis investigates enclitic possessive constructions (EPCs) that are a widespread and frequently used construction among Southern Italian dialects (SIDs). In general, EPCs display the structure N-EP where the N is a (singular) kinship noun and the EP the enclitic possessive directly attached to the kinship noun. However, there is a huge variation among SIDs as well as within the system of a specific dialect. The aim of the present work is twofold. The empirical part contributes new data to this topic as well as a detailed and organized overview of (micro-) variational observations from data of different sources including for example the linguistic maps of the AIS (Atlante Italo-Svizzero). The main aspects of variation are (a) the presence or absence of an obligatory article (D – N-EP vs. N-EP), (b) the possibility of plural kinship noun-EPCs and (c) the compatibility of a specific person-EP with a specific kinship noun within a dialect. Based on the empirical findings, the syntactic part proposes a syntactic analysis for EPCs focusing on the following research questions: 1) In some dialects, singular kinship noun-EPCs display an obligatory article with the 3SG.EP. What is the reason for this article-based person split (1st and 2nd vs. 3rd)? And further, how are both structures, with and without an article, represented in the syntax, i.e. in DP and PossP? 2) In some dialects, plural kinship nouns are allowed to occur in EPCs, and in others, they are disallowed. With respect to this dichotomy, what is the role of NumP? 3) Kinship nouns are relational and express inalienability. How can this property be captured in the syntax? I argue that the article-based person split is due to the deictic properties of the possessor-persons, meaning that 1SG.EPs and 2SG.EPs need to be bound by the speaker’s coordinates in the left periphery of the clause, whereas 3SG.EPs do not. As a consequence, 1SG and 2SG EPCs move to the highest position, i.e. to D°, and 3SG EPCs can stay lower in the structure, i.e. in Poss°. Based on this dichotomy, I argue that both D° and Poss° can host EPCs. In order to capture the (im)possibility of plural kinship nouns-EPCs, I argue that NumP, as a parametrised position, can block or allow further movement of the kinship noun to Poss° (and to D°). With respect to the relational nature of kinship nouns I propose that they are base-generated within the complement position of a relator phrase (RP), and EPs in Poss°. In order to derive EPCs, the kinship nouns must move out of their position. The kinship noun lands in NumP, the position where further movement is probably blocked. If further movement is allowed, the kinship noun merges to the left of the EP, resulting in a complete EPC in Poss°. The last leg of the movement to D° depends on the presence of absence of an obligatory article. The phenomenon of EPCs displays a huge variation among SIDs and needs to be investigated from different perspectives and different linguistic areas. The present work contributes to the puzzle of EPCs new data and a syntactic analysis.
We study the Wigner function for massive spin-1/2 fermions in electromagnetic fields. The Wigner function is analytically solved in five cases when electromagnetic fields are constants. For a general space-time dependent field configuration, we use the method of semi-classical expansion and solved the Wigner function at linear order in the Planck's constant. At the same order, we obtained a generalized Boltzmann equation for particle distribution, and a generalized BMT equation for spin polarization. Using the Wigner function, we calculated some physical quantities in a thermal equilibrium system.