Pinning of Fermionic Occupation Numbers

The Pauli exclusion principle is a constraint on the natural occupation numbers of fermionic states. It has been suspected since at least the 1970's, and only proved very recently, that there is a multitude of further constraints on these numbers, generalizing the Pauli principle. Here, we provide the first analytic analysis of the physical relevance of these constraints. We compute the natural occupation numbers for the ground states of a family of interacting fermions in a harmonic potential. Intriguingly, we find that the occupation numbers are almost, but not exactly, pinned to the boundary of the allowed region (quasi-pinned). The result suggests that the physics behind the phenomenon is richer than previously appreciated. In particular, it shows that for some models, the generalized Pauli constraints play a role for the ground state, even though they do not limit the ground-state energy. Our findings suggest a generalization of the Hartree-Fock approximation

More efficient time integration for Fourier pseudo-spectral DNS of incompressible turbulence

Time integration of Fourier pseudo-spectral DNS is usually performed using the classical fourth-order accurate Runge--Kutta method, or other methods of second or third order, with a fixed step size. We investigate the use of higher-order Runge-Kutta pairs and automatic step size control based on local error estimation. We find that the fifth-order accurate Runge--Kutta pair of Bogacki \& Shampine gives much greater accuracy at a significantly reduced computational cost. Specifically, we demonstrate speedups of 2x-10x for the same accuracy. Numerical tests (including the Taylor-Green vortex, Rayleigh-Taylor instability, and homogeneous isotropic turbulence) confirm the reliability and efficiency of the method. We also show that adaptive time stepping provides a significant computational advantage for some problems (like the development of a Rayleigh-Taylor instability) without compromising accuracy

Friedrich Nietzsche\u27s reception as a marker of American intellectual culture : Crane Brinton and Walter Kaufmann\u27s interpretations during the World War II and postwar eras

Friedrich Nietzsche\u27s philosophy has endured a torrent of both insightful analysis and faulty interpretation in America. This thesis seeks to examine a comer of this intellectual history, specifically some of the connections between political events and American readers\u27 reception of Nietzsche\u27s work. Chapter 1 introduces the study, arguing that an intellectual row created during the World War I era persisted into the Depression and World War II years. Chapter 2 analyzes Crane Brinton\u27s Nietzsche and that historian\u27s attempts to explain Nietzsche in terms of World War II politics, namely fascist thought. Brinton\u27s efforts to establish a link between Nietzsche and contemporary ideology are presented as representative of the larger discourse during the Second World War. Chapter 3 explores the contrasting position of Walter Kaufmann\u27s fundamental reevaluation of Nietzsche\u27s philosophy in Nietzsche: Philosopher, Psychologist, Antichrist, appearing in 1950. Kaufmann\u27s interpretation, a more sober and relativistic account, includes a major effort to divorce Nietzsche from his classification as a proto- Nazi. Chapter 4 concludes that Kaufmann\u27s challenge to reconsider Nietzsche-a movement away from the failings of Brinton\u27s interpretation-not only profoundly changed the thinker\u27s academic and popular legacy, but also reflects a discipline-wide reevaluation of the connections between academic discourse and political motion and offers lessons for exploring this relationship within contemporary scholarship

The (strong) Liouville property for a class of non-local operators

We prove a necessary and sufficient condition for the Liouville and strong Liouville properties of the infinitesimal generator of a L\'evy process and subordinate L\'evy processes. Combining our criterion with the necessary and sufficient condition obtained by Alibaud et al., we obtain a characterization of (orthogonal subgroup of) the set of zeros of the characteristic exponent of the L\'evy process.Comment: arXiv admin note: text overlap with arXiv:1909.0123

Effect of mixing and spatial dimension on the glass transition

We study the influence of composition changes on the glass transition of binary hard disc and hard sphere mixtures in the framework of mode coupling theory. We derive a general expression for the slope of a glass transition line. Applied to the binary mixture in the low concentration limits, this new method allows a fast prediction of some properties of the glass transition lines. The glass transition diagram we find for binary hard discs strongly resembles the random close packing diagram. Compared to 3D from previous studies, the extension of the glass regime due to mixing is much more pronounced in 2D where plasticization only sets in at larger size disparities. For small size disparities we find a stabilization of the glass phase quadratic in the deviation of the size disparity from unity.Comment: 13 pages, 8 figures, Phys. Rev. E (in print

Glass transition of binary mixtures of dipolar particles in two dimensions

We study the glass transition of binary mixtures of dipolar particles in two dimensions within the framework of mode-coupling theory, focusing in particular on the influence of composition changes. In a first step, we demonstrate that the experimental system of K\"onig et al. [Eur. Phys. J. E 18, 287 (2005)] is well described by point dipoles through a comparison between the experimental partial structure factors and those from our Monte Carlo simulation. For such a mixture of point particles we show that there is always a plasticization effect, i.e. a stabilization of the liquid state due to mixing, in contrast to binary hard disks. We demonstrate that the predicted plasticization effect is in qualitative agreement with experimental results. Furthermore, also some general properties of the glass transition lines are discussed.Comment: 12 pages, 8 figures, J. Non-Cryst. Solids (in print

Stress and Growth Related Keratinocyte Pathways

Cellular stress and damage response mechanisms play a crucial role in physiological defense against hyperproliferative diseases, genotoxic injury, mutations and malignancy. An important first step in the cellular stress response is upregulation of immediate early genes that initiate and coordinate subsequent cellular events. IEX-1 is a novel immediate early gene that has been shown to be induced by gamma irradiation, phorbol ester treatment and ultraviolet irradiation. Goal of this thesis was to more specifically characterize the role of IEX-1 in keratinocytes. Special emphasis was directed to elucidating the cellular response to stress and mitogenic stimulation and the role of IEX-1 in mediating apoptosis as well as localizing the protein within the cell during these events. By northern blot analysis, it could be shown that gamma irradiation of primary human keratinocytes results in a time dependent, rapid induction of IEX-1 expression followed by prompt downregulation, similar to previous findings in a squamous cell carcinoma cell line. In addition, UV-irradiation or treatment with the reactive oxygen species hydrogen peroxide also induced IEX-1 expression rapidly and transiently. Further incubation with the mitogenic factor for keratinocyte Epidermal Growth Factor (EGF) resulted in increased steady state levels of IEX-1 mRNA. Compared to normal keratinocytes, similar observations were made in the non-tumorigenic keratinocyte cell line HaCaT. Regulation of IEX-1 gene expression by the EGF-Receptor (EGFR) was investigated using an IEX-1-promoter-luciferase-reporter-gene assay and blockage of EGFR by the highly specific EGFR-tyrosine kinase inhibitor PD153035. Blockage of the receptor was followed by a marked decrease in IEX-1 promoter activity. Effects of IEX-1 overexpression in HaCaT cells were investigated. IEX-1 overexpression enhanced proliferation, as confirmed by [3H]-thymidine incorporation assay. To examine the effects of IEX-1 on apoptosis induced by various agents, IEX-1 over-expressing HaCaT were challenged with ultraviolet radiation, the DNA damaging agent camptothecin or serum-deprival. Cell survival, caspase 3-activity and nucleosome formation were measured to assess apoptosis. There was no difference observed in baseline apoptotic activity of cells cultured under non-stressed conditions, when comparing the IEX-1 overexpressing and the control cell line. However, upon stress-induction, the IEX-1 overexpressing cells showed markedly higher levels of apoptosis. Data characterizing the intracellular localization of IEX-1 were obtained by immunohistochemical staining as well as by molecular biological methods. IEX-1 was predominantly located within the cell nucleus, forming several intranuclear patches. Treatment with various stress-inducing agents did not significantly alter the localization or cause translocation of the IEX-1 protein. Distribution of IEX-1 within the skin and epidermis was assessed by immunocytochemistry of human skin specimens and revealed predominant localization of IEX-1 within the nucleus and cytoplasm of the basal epidermal and suprabasal layers. These findings implicate IEX-1 in the control of apoptosis upon cell stress as well as promotion of cell replication during favorable growth conditions. The function of IEX-1 seems to be closely linked to the differentiation status of the keratinocyte. As an immediate early gene product, IEX-1 is a novel regulator of keratinocyte growth and survival, similar to other critical cell cycle control proteins, such as p53, p21Waf1, c-myc and related proteins. This suggests that IEX-1 is another crucial element in the pattern of regulatory pathways of cell growth and defense against malignant transformation.Zelluläre Mechanismen als Antwort auf Zellstress oder Zellschäden spielen eine wesentliche Rolle in der physiologischen Verteidigungsstrategie gegen hyperproliferative Krankheiten, genotoxische Schäden, Mutationen oder maligne Entartung. Die Expression von Immediate Early Genen, die nachfolgende zelluläre Ereignisse initiieren und koordinieren, ist ein wichtiger erster Schritt der zellulären Stressantwort. IEX-1 ist ein vor kurzem entdecktes Immediate Early Gen, von dem gezeigt werden konnte, dass es durch die Einwirkung von Gammastrahlen, Phorbolestern und Ultraviolettstrahlung induziert wird. Ziel dieser Arbeit war es, die Funktion von IEX-1 in der Stressantwort von Keratinozyten genauer zu charakterisieren. Nicht nur die zelluläre Antwort auf Stress, sondern auch die mitogene Stimulation und die Rolle von IEX-1 in Bezug auf Apoptosereaktionswege sollten untersucht werden. Weiteres Interesse galt der Analyse der IEX-1-Proteinlokalisation während dieser Ereignisse. Mit Hilfe des Northern Blot Verfahrens konnte gezeigt werden, dass IEX-1 nach Gamma-Bestrahlung von primären menschlichen Keratinozyten innerhalb von Minuten induziert und dann sehr rasch wieder herunter geregelt wird, ähnlich wie schon zuvor mit einer Keratinozyten-Tumorzelllinie gezeigt wurde. Außerdem bewirkte UV-Strahlung und Behandlung mit reaktiven Sauerstoffradikalen eine rasche, aber vorübergehende Induktion von IEX-1. Zusätzlich rief die Inkubation der Keratinozyten mit epidermal growth factor (EGF) erhöhte steady state Spiegel von IEX-1 mRNA hervor. Ähnliche Beobachtungen konnten an der HaCaT-Zelllinie, einer nicht-tumorigenen Keratinozytenlinie gemacht werden. Die Regulation der IEX-1-Genexpression durch den epidermal growth factor-Rezeptor (EGFR) wurde mittels eines IEX-1-Promotor – Luciferase Assays untersucht. Dabei wurde der EGF-Rezeptor mit dem hochspezifischen EGFR-Tyrosinkinaseinhibitor PD153035 blockiert. Der Rezeptorblockade folgte ein starker Rückgang der IEX-1-Promotoraktivität. Die Auswirkungen der Überexpression von IEX-1 in HaCaT-Zellen wurde untersucht. Wachstumsstudien mit [3H]-Thymidin-Inkorporationsassays ergaben, dass IEX- Überexpression das Wachstum beschleunigt. Um die Auswirkungen von IEX-1 auf die Apoptose zu untersuchen, wurden IEX-1 überexprimierende HaCaT-Zellen mit ultravioletter Bestrahlung, dem DNA-toxischen Agens Captothecin oder Serumentzug behandelt. Die Apoptoserate wurde mittels Caspase-3-Enzymaktivität und Oligonucleosomenbildung im Zellplasma quantifiziert. Die entsprechenden Assays konnten erstmalig für adhärente Keratinozytenkulturen etabliert werden. Unter normalen Wachstumsbedingungen ohne Stress konnte kein Unterschied in der basalen Apoptoserate zwischen IEX-1-überexprimierenden Zellen und Kontrollzellen beobachtet werden. Wurden die Zellen jedoch Stress ausgesetzt, dann trat in den IEX-1-überexprimierenden Zellkulturen in erhöhtem Maße Apoptose auf. Das IEX-1-Protein konnte mit immunhistochemischen sowie molekularbiologischen Methoden vorwiegend im Zellkern lokalisiert werden, wo es sich in unterschiedlicher Verteilung zeigte. Stressinduzierende Behandlung der Zellen konnte keine Translokation des Proteines oder eine Veränderung im Verteilungsmuster bewirken. Untersuchung an menschlicher Epidermis mittels immunhistochemischer Färbung zeigte, dass IEX-1 hauptsächlich in den basalen und suprabasalen Schichten der Epidermis exprimiert wird. Mit diesen Ergebnissen konnte erstmals gezeigt werden, dass IEX-1 eine wichtige Rolle sowohl in der Kontrolle der Apoptose als Folge von Zellstress, als auch in der Vermittlung von Zellreplikation unter optimalen Wachstumsbedingungen zukommt. Die Wirkung von IEX-1 scheint dabei eng an den Differenzierungsstatus der Keratinozyten gebunden zu sein. Als Produkt eines Immediate early Gens spielt IEX-1 eine Rolle in der Vermittlung von Keratinozytenwachstum und Keratinozytenüberleben, ähnlich wie die wichtigen Zellzyklusproteine p53, p21Waf1,c-myc und andere verwandte Proteine. Damit zeichnet es sich als ein weiterer elementarer Baustein im Mosaik der Reaktionswege zur Regulierung von Zellwachstum und Bekämpfung von maligner Entartung ab

Population Dynamics with Nonlinear Diffusion

We consider reaction diffusion models in population dynamics where the per capita growth rate is a logistic type or a weak Allee type. In particular, we study the effects of nonlinear diffusion (arising due to aggregative population movements) on the steady states. We obtain our results via the quadrature method

Reclaiming Vacant Houses & Preventing Foreclosure: Lessons from LISCs New York State Vacants Initiative

The housing instability caused by COVID has continued into 2022, even as foreclosure moratoria end at federal and state levels around the country. This report, Reclaiming Vacant Houses & Preventing Foreclosure: Lessons from LISC's New York State Vacants Initiative, a collaboration of LISC and the Urban Institute, provides lessons and evidence of outcomes of a path-breaking law and LISC initiative in reducing vacant houses and preventing foreclosures in jurisdictions across New York State