Level density of a Fermi gas and integer partitions: a Gumbel-like finite-size correction

We investigate the many-body level density of gas of non-interacting fermions. We determine its behavior as a function of the temperature and the number of particles. As the temperature increases, and beyond the usual Sommerfeld expansion that describes the degenerate gas behavior, corrections due to a finite number of particles lead to Gumbel-like contributions. We discuss connections with the partition problem in number theory, extreme value statistics as well as differences with respect to the Bose gas.Comment: 5 pages, 1 figure, one figure added, accepted for publication in Phys. Rev.

How Complicated Can It Be? The Link Between APOL1 Risk Variants and Lipoprotein Heterogeneity in Kidney and Cardiovascular Diseases.

The beginning of human apolipoprotein L1 study (gene: APOL1; protein: ApoL1) originated from the identification of circulating ApoL1 as an interacting protein of ApoA1 and a minor component of high-density lipoprotein subfraction 3 (HDL3) in 1997 [1]. In the past 18 years, ApoL1 has been investigated in the context of complex human diseases such as African sleeping sickness, schizophrenia, host innate immunity, cancer, hyperlipidemia, cardiovascular diseases, stroke and type 2 diabetes [2–10]. A major breakthrough, however, was the documentation of two haplotypes of APOL1, harboring three coding-sequence mutations as risk variants associated with non-diabetic chronic kidney diseases (CKD) in African Americans [5, 6]. The first one, termed G1, is a two non-synonymous SNP haplotype [rs73885319 (A \u3e G; p.S342G) and rs60910145 (G \u3e T; p.I384M)]. The second one, termed G2, is a two codon deletion haplotype rs71785313 (6-bp in frame deletion; p.ΔN388Y389) [4, 5]. These two coding-sequence variants have been discovered mainly in kidney disease patients of African ancestry and linked to the pathogenesis of primary focal and segmental glomerulosclerosis, hypertension-attributed kidney disease and HIV-associated nephropathy (HIVAN), under a recessive inheritance pattern [3, 7, 10]. Moreover, these APOL1 variants and African American recipient ethnicity have been shown to associate with kidney transplant rejection and allograft failure [11–13]. Importantly, the expression of ApoL1 has been detected in renal proximal tubular epithelial cells, podocytes, medium-sized arteries, arteriolar endothelial cells and pre-glomerular vascular structures [3, 14, 15]. Thus, there is no doubt or controversy regarding the notion that the expression of APOL1 risk alleles in kidney cells is associated with the development and progression of non-diabetic CKD in African Americans. In fact, we and others have shown that interferon-α, -β and -γ and TNF-α can induce the expression of ApoL1 in endothelial cells and overexpression of ApoL1 can lead to autophagy- and/or necrosis-associated cell death in a variety of cell types, including endothelial cells and podocytes [15–19]. However, the role of ApoL1 in the outcome of cardiovascular diseases is a much more controversial topic [20]. Some studies suggest that the APOL1 risk alleles have an adverse effect [8], while others failed to detect an association between the risk alleles and these cardiovascular events [9], or showed improved survival in patients with two risk alleles [10]. Moreover, the potential role that extracellular/circulating ApoL1 might have on systemic endothelial and/or kidney cells is currently unknown. It is worth noting that besides being a component of HDL, ApoL1 is also a component of very low density lipoproteins (VLDL) and LDL [21]. This fact, however, has been frequently overlooked and the role of ApoL1 in VLDL and LDL has not been explored. In this issue, Gutierrez et al. [22] utilized a case–control sample of African Americas who were part of the Sea Islands Genetics Network (SIGNET) and assessed the relationship between the APOL1 risk variants, G1 and G2, and the circulating levels of different lipoproteins and sizes of HDL subclasses measured by nuclear magnetic resonance (NMR) spectroscopy. Using this well-established NMR technique, which is based on the assessment of distinct methyl groups of lipid species in plasma samples [23, 24], they found a modest increase of small-size HDL particles (small HDL) in the circulation of patients carrying the APOL1 G1/G2 risk alleles, independently of age, sex, diabetes and percentage of African ancestry. There were no significant differences in large or medium HDL, VLDL or LDL concentrations observed by APOL1 genotype in this study. Although the classification of large, medium and small of HDL is different from that of HDL 1, 2 and 3 subfractions defined by the density/density centrifugation [25–28], the small HDL should be lipid-poor and high density similar to, if not the same as, HDL3, of which ApoL1 is a component [1]. However, in this study the levels of ApoL1 in plasma samples were not measured and therefore cannot be correlated to the levels of small HDL or other lipoprotein particles. The results of Gutierrez et al. may be clinically relevant, since they suggest that the APOL1 genotype could play a direct role in determining the circulating concentration of small HDL, which have been associated with renal and cardiovascular diseases [7–10, 27]. However, as discussed in their article, these findings should be interpreted with caution. The authors propose that the APOL1 risk variants could contribute to the increase prevalence of renal disease by facilitating the formation of circulating HDL subpopulations with pro-atherogenic properties. Nonetheless, the difference in the circulating levels of small HDL between subjects with zero and two APOL1 risk alleles was modest (0.9 µmol/L), and although a previous study found that changes of this magnitude could be associated with albuminuria [27], no differences were found in the prevalence of CKD, albuminuria or other markers of cardiometabolic status across all the APOL1 categories in the subjects of this study [22]. In addition, the difference in small HDL concentration between individuals with one risk allele versus two risk alleles was minor (0.2 μmol/L) and very unlikely to be clinically relevant. Moreover, if two APOL1 risk alleles and higher circulating concentrations of small HDL interact to precipitate CKD, one should ask why two APOL1 risk alleles do not increase risk of diabetic nephropathy in African Americans with elevated HDL3. If the role of APOL1 rick alleles is to increase the concentration of small HDL (or HDL3), then adding elevated HDL3 is redundant; if the small HDL (or HDL3) are elevated already due to other factors, then APOL1 rick alleles cannot play an additional role by increasing small HDL (or HDL3). On the other hand, it is well known that once diabetic nephropathy is established, the progression of the renal disease is accelerated in patients carrying two APOL1 risk alleles [7]. In summary, given the negligible difference reported between the circulating levels of small HDL in patients carrying one versus two risk alleles (0.2 μmol/L), these changes are very unlikely to explain the increase risk of CKD conferred only by two risk alleles. As an alternative explanation, Gutierrez et al. argue that the elevated levels of small HDL could be due to changes in renal metabolic pathways. In this regard, a previous study showed that cubilin (gene: CUBN; protein: cubilin), an endocytic receptor highly expressed in renal proximal tubules, mediates the uptake of albumin and filtered forms of ApoA1-HDL [29]. Moreover, CUBN heterozygous deficient mice and transgenic mice overexpressing human cubilin showed either decreased or elevated levels of ApoA1, HDL cholesterol and HDL3 particles, respectively [29]. Nonetheless, the subjects carrying two risk alleles of APOL1 in the Gutierrez study showed only a minor increase in the circulating concentration of small HDL, suggesting that this isolated change is unlikely to be the result of renal metabolism. Taken together, the findings of Gutierrez et al. [22] add more fuel to the ongoing controversy regarding the association of APOL1 G1/G2 risk status with cardiovascular outcome among African Americans. However, if one speculates that the APOL1 risk alleles may directly modify the circulating levels of small HDL and/or other factors and induce a pro-atherogenic state that precipitates CKD and cardiovascular complications, then one should begin to answer the following several questions. (i) Why are the APOL1 risk variants not associated with an increased prevalence of diabetic nephropathy in African Americans? (ii) Would the APOL1 risk alleles alter the synthesis and function of other proteins in HDL3, VLDL and VDL? (iii) How do the circulating ApoL1 mutant proteins interact with the plasma membrane and initiate a signal transduction pathway from outside to inside of the targeted cell? (iv) What mechanisms modulate the transport of circulating ApoL1 mutant proteins inside the cells and its interaction with intracellular ApoL1 and/or other intracellular proteins, for example, apolipoprotein L6 (ApoL6), an ApoL1-related protein, which when overexpressed, induces atherosclerotic apoptosis [30]? Finally, as the expression of ApoL1 can be induced by inflammatory cytokines and intracellular accumulation of ApoL1 can initiate autophagy and cell death in endothelia cells, the crosstalk between inflammation, autophagy and cell death mediated by the overexpression of ApoL1 should be much more intensively investigated before one can properly interpret the meaning of these findings reported by Gutierrez et al. [22]

Coulomb's law corrections from a gauge-kinetic mixing

We study the static quantum potential for a gauge theory which includes the mixing between the familiar photon $U(1)_{QED}$ and a second massive gauge field living in the so-called hidden-sector $U(1)_h$. Our discussion is carried out using the gauge-invariant but path-dependent variables formalism, which is alternative to the Wilson loop approach. Our results show that the static potential is a Yukawa correction to the usual static Coulomb potential. Interestingly, when this calculation is done inside a superconducting box, the Coulombic piece disappears leading to a screening phase.Comment: 4 page

Expanding Lie (super)algebras through abelian semigroups

We propose an outgrowth of the expansion method introduced by de Azcarraga et al. [Nucl. Phys. B 662 (2003) 185]. The basic idea consists in considering the direct product between an abelian semigroup S and a Lie algebra g. General conditions under which relevant subalgebras can systematically be extracted from S \times g are given. We show how, for a particular choice of semigroup S, the known cases of expanded algebras can be reobtained, while new ones arise from different choices. Concrete examples, including the M algebra and a D'Auria-Fre-like Superalgebra, are considered. Finally, we find explicit, non-trace invariant tensors for these S-expanded algebras, which are essential ingredients in, e.g., the formulation of Supergravity theories in arbitrary space-time dimensions.Comment: 42 pages, 8 figures. v2: Improved figures, updated notation and terminolog

Dynamical noise can enhance high-order statistical structure in complex systems

Recent research has provided a wealth of evidence highlighting the pivotal role of high-order interdependencies in supporting the information-processing capabilities of distributed complex systems. These findings may suggest that high-order interdependencies constitute a powerful resource that is, however, challenging to harness and can be readily disrupted. In this paper we contest this perspective by demonstrating that high-order interdependencies can not only exhibit robustness to stochastic perturbations, but can in fact be enhanced by them. Using elementary cellular automata as a general testbed, our results unveil the capacity of dynamical noise to enhance the statistical regularities between agents and, intriguingly, even alter the prevailing character of their interdependencies. Furthermore, our results show that these effects are related to the high-order structure of the local rules, which affect the system's susceptibility to noise and characteristic times-scales. These results deepen our understanding of how high-order interdependencies may spontaneously emerge within distributed systems interacting with stochastic environments, thus providing an initial step towards elucidating their origin and function in complex systems like the human brain.Comment: 8 pages, 4 figures, 2 table

Determinación de autovalores usando el método optimizado de Rayleigh-Ritz y "pseudo" desarrollos de Fourier

Hace algo más de un siglo Lord Rayleigh sugirió el uso de un parámetro de optimización en las funciones coordenadas polinómicas a ser utilizadas en la aplicación de su actualmente famoso método, teniendo como meta el minimizar el autovalor determinado. Tres décadas después el célebre analista y diseñador de sistemas mecánicos, Stodola, utilizó este enfoque al deteminar la frecuencia fundamental de un álabe. Linus Pauling y Bright-Wilson implementaron el enfoque utilizando funciones exponenciales en problemas de mecánica cuántica y Timoshenko y Goodier también lo hicieron, utilizando también funciones exponenciales, en un problema de torsión de barras elásticas. En este trabajo se presentan aplicaciones del criterio de Rayleigh, pero difiriendo del enfoque de los autores citados, se usan funciones trigonométricas que contienen parámetros de optimización en su argumento, tomando como sistemas mecánicos vibrantes casos de placas o losas rectangulares con un borde libre.Peer Reviewe

Level density of a Fermi gas: average growth and fluctuations

We compute the level density of a two--component Fermi gas as a function of the number of particles, angular momentum and excitation energy. The result includes smooth low--energy corrections to the leading Bethe term (connected to a generalization of the partition problem and Hardy--Ramanujan formula) plus oscillatory corrections that describe shell effects. When applied to nuclear level densities, the theory provides a unified formulation valid from low--lying states up to levels entering the continuum. The comparison with experimental data from neutron resonances gives excellent results.Comment: 4 pages, 1 figur

Aristonectes quiriquinensis, sp. nov., a new highly derived elasmosaurid from the upper Maastrichtian of central Chile

This paper describes a new species of elasmosaurid plesiosaur, Aristonectes quiriquinensis, sp. nov., based on a partial skeleton recovered from upper Maastrichtian beds of the Quiriquina Formation of central Chile. The material described here consists of two skeletons, one collected near the village of Cocholgue, and a second juvenile specimen from Quiriquina Island. Prior to these finds, Aristonectes was viewed as a monospecific genus, including only the enigmatic Aristonectes parvidens, the holotype of which consists of an incomplete skull and incomplete postcranium. Other material referred to the genus includes an incomplete juvenile skull and other postcranial material from the upper Maastrichtian of Antarctica, as well as a partial skull from the Quiriquina Formation of central Chile. The relationships of Aristonectes have been controversial, with competing theories assigning the genus to Cryptoclididae, Elasmosauridae, and Aristonectidae; however, there is a developing consensus that Aristonectes is a derived elasmosaurid, and this paper gives strong evidence for this view. Comparison of the specimen here studied with the holotype of A. parvidens demonstrates that A. quiriquinensis is a distinct species. The completeness of the adult skeleton allows the first confident size estimates for adult Aristonectes. It is a large plesiosaurian with a relatively large skull with numerous homodont teeth, a moderately long and laterally compressed neck, and relatively narrow trunk, with slender and elongate forelimbs. The two specimens are restricted to the upper Maastrichtian of central Chile, posing questions concerning the austral circumpolar distribution of different elasmosaurids towards the end of the Cretaceous.Fil: Otero, Rodrigo A.. Universidad de Chile; ChileFil: Soto Acuña, Sergio. Museo Nacional de Historia Natural de Santiago; Chile. Universidad de Chile; ChileFil: O'Keefe, Frank Robin. Marshall University; Estados UnidosFil: O'gorman, Jose Patricio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Naturales y Museo; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Naturales y Museo. División Paleontología Vertebrados; ArgentinaFil: Stinnesbeck, Wolfgang. Heidelberg University; AlemaniaFil: Suárez, Mario E.. Museo Nacional de Historia Natural de Santiago; Chile. Universidad de Chile; ChileFil: Rubilar-Rogers, David. Museo Nacional de Historia Natural de Santiago; Chile. Universidad de Chile; ChileFil: Salazar, Christian. Museo Nacional de Historia Natural de Santiago; Chile. Universidad de Chile; ChileFil: Quinzio Sinn, Luis Arturo. Universidad de Concepción; Chil

Cellulosomics, a gene-centric approach to investigating the intraspecific diversity and adaptation of Ruminococcus flavefaciens within the rumen

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