Asymptotic behavior of age-structured and delayed Lotka-Volterra models

In this work we investigate some asymptotic properties of an age-structured Lotka-Volterra model, where a specific choice of the functional parameters allows us to formulate it as a delayed problem, for which we prove the existence of a unique coexistence equilibrium and characterize the existence of a periodic solution. We also exhibit a Lyapunov functional that enables us to reduce the attractive set to either the nontrivial equilibrium or to a periodic solution. We then prove the asymptotic stability of the nontrivial equilibrium where, depending on the existence of the periodic trajectory, we make explicit the basin of attraction of the equilibrium. Finally, we prove that these results can be extended to the initial PDE problem.Comment: 29 page

Chiral crystals in strong-coupling lattice QCD at nonzero chemical potential

We study the effective action for strong-coupling lattice QCD with one-component staggered fermions in the case of nonzero chemical potential and zero temperature. The structure of this action suggests that at large chemical potentials its ground state is a crystalline `chiral density wave' that spontaneously breaks chiral symmetry and translation invariance. In mean-field theory, on the other hand, we find that this state is unstable. We show that lattice artifacts are partly responsible for this, and suggest that if this phase exists in QCD, then finding it in Monte-Carlo simulations would require simulating on relatively fine lattices. In particular, the baryon mass in lattice units, m_B, should be considerably smaller than its strong-coupling limit of m_B~3.Comment: 33 pages, 8 figure

Hilbert Space of Isomorphic Representations of Bosonized Chiral QCD2QCD_2

We analyse the Hilbert space structure of the isomorphic gauge non-invariant and gauge invariant bosonized formulations of chiral $QCD_2$ for the particular case of the Jackiw-Rajaraman parameter $a = 2$. The BRST subsidiary conditions are found not to provide a sufficient criterium for defining physical states in the Hilbert space and additional superselection rules must to be taken into account. We examine the effect of the use of a redundant field algebra in deriving basic properties of the model. We also discuss the constraint structure of the gauge invariant formulation and show that the only primary constraints are of first class.Comment: LaTeX, 19 page

Cinacalcet Treatment of Primary Hyperparathyroidism

Although parathyroidectomy remains the only curative approach to most primary hyperparathyroidism cases, medical treatment with cinacalcet HCl has been proven to be a reasonable alternative for several patient subgroups. Cinacalcet almost always controls hypercalcemia and hypophosphatemia sufficiently. PTH levels are lowered, and cognitive parameters improve. While an increase in bone mineral density DEXA scan scores was not demonstrated in cinacalcet trials, the same applies to more than half of patients after parathyroidectomy. Medical therapy should be first choice in patients with hyperplasia in all glands rather than an isolated adenoma (10–15%), patients with persisting HPT following unsuccessful surgery or inoperable cases due to comorbidities, and patients detected in lab screens for hypercalcemia before developing symptoms who should be treated early but are usually reluctant to undergo surgery. Nephrolithiasis was not found to occur more frequently in cinacalcet trial groups, but urine calcium excretion as one major risk factor of this complication of primary HPT may increase on cinacalcet. Patients carrying the rs1042636 polymorphism of the calcium-sensing receptor gene respond more sensitively to cinacalcet and have a higher risk of calcium stone formation. Cinacalcet is usually administered twice daily but three or four doses per day should be discussed to mimic the beneficial pulsatile PTH-pattern

The Lippmann–Schwinger Formula and One Dimensional Models with Dirac Delta Interactions

We show how a proper use of the Lippmann–Schwinger equation simplifies the calculations to obtain scattering states for one dimensional systems perturbed by N Dirac delta equations. Here, we consider two situations. In the former, attractive Dirac deltas perturbed the free one dimensional Schrödinger Hamiltonian. We obtain explicit expressions for scattering and Gamow states. For completeness, we show that the method to obtain bound states use comparable formulas, although not based on the Lippmann–Schwinger equation. Then, the attractive N deltas perturbed the one dimensional Salpeter equation. We also obtain explicit expressions for the scattering wave functions. Here, we need regularisation techniques that we implement via heat kernel regularisation

Pathogenicity of missense variants affecting the collagen IV α5 carboxy non-collagenous domain in X-linked Alport syndrome.

X-linked Alport syndrome is a genetic kidney disease caused by pathogenic COL4A5 variants, but little is known of the consequences of missense variants affecting the NC1 domain of the corresponding collagen IV α5 chain. This study examined these variants in a normal (gnomAD) and other databases (LOVD, Clin Var and 100,000 Genomes Project) to determine their pathogenicity and clinical significance. Males with Cys substitutions in the collagen IV α5 NC1 domain reported in LOVD (n = 25) were examined for typical Alport features, including age at kidney failure. All NC1 variants in LOVD (n = 86) were then assessed for structural damage using an online computational tool, Missense3D. Variants in the ClinVar, gnomAD and 100,000 Genomes Project databases were also examined for structural effects. Predicted damage associated with NC1 substitutions was then correlated with the level of conservation of the affected residues. Cys substitutions in males were associated with the typical features of X-linked Alport syndrome, with a median age at kidney failure of 31 years. NC1 substitutions predicted to cause structural damage were overrepresented in LOVD (p < 0.001), and those affecting Cys residues or 'buried' Gly residues were more common than expected (both p < 0.001). Most NC1 substitutions in gnomAD (88%) were predicted to be structurally-neutral. Substitutions affecting conserved residues resulted in more structural damage than those affecting non-conserved residues (p < 0.001). Many pathogenic missense variants affecting the collagen IV α5 NC1 domain have their effect through molecular structural damage and 3D modelling is a useful tool in their assessment

The Hagedorn spectrum and large NcN_c QCD in 2+1 and 3+1 dimensions

We show that a Hagedorn spectrum (i.e., spectrum where the number of hadrons grows exponentially with the mass) emerges automatically in large $N_c$ QCD in 2+1 and 3+1 dimensions. The approach is based on the study of Euclidean space correlation functions for composite operators constructed from quark and gluon fields and exploits the fact that the short time behavior of the correlators is known in QCD. The demonstration relies on one critical assumption: that perturbation theory accurately describes the trace of the logarithm of a matrix of point-to-point correlation functions in the regime where the perturbative corrections to the asymptotically free value are small.Comment: 18 pages, 5 figure

Hamiltonian Embedding of SU(2) Higgs Model in the Unitary Gauge

Following systematically the generalized Hamiltonian approach of Batalin, Fradkin and Tyutin (BFT), we embed the second-class non-abelian SU(2) Higgs model in the unitary gauge into a gauge invariant theory. The strongly involutive Hamiltonian and constraints are obtained as an infinite power series in the auxiliary fields. Furthermore, comparing these results with those obtained from the gauged second class Lagrangian, we arrive at a simple interpretation for the first class Hamiltonian, constraints and observables.Comment: 13 pages, Latex, no figure

Lattice Artefacts In The Non-Abelian Debye Screening Mass In One Loop Order

We compute the electric screening mass in lattice QCD with Wilson fermions at finite temperature and chemical potential to one-loop order, and show that lattice artefacts arising from a finite lattice spacing result in an enhancement of the screening mass as compared to the continuum. We discuss the magnitude of this enhancement as a function of the temperature and chemical potential for lattices with different number of lattice sites in the temporal direction that can be implemented in lattice simulations. Most of the enhancement is found to be due to the fermion loop contribution.Comment: 23 pages, 8 figures, LaTe

VEGF preconditioning leads to stem cell remodeling and attenuates age-related decay of adult hippocampal neurogenesis

Several factors are known to enhance adult hippocampal neurogenesis but a factor capable of inducing a long-lasting neurogenic enhancement that attenuates age-related neurogenic decay has not been described. Here, we studied hippocampal neurogenesis following conditional VEGF induction in the adult brain and showed that a short episode of VEGF exposure withdrawn shortly after the generation of durable new vessels (but not under conditions where newly made vessels failed to persist) is sufficient for neurogenesis to proceed at a markedly elevated level for many months later. Continual neurogenic increase over several months was not accompanied by accelerated exhaustion of the neuronal stem cell (NSC) reserve, thereby allowing neurogenesis to proceed at a markedly elevated rate also in old mice. Neurogenic enhancement by VEGF preconditioning was, in part, attributed to rescue of age-related NSC quiescence. Remarkably, VEGF caused extensive NSC remodelling manifested in transition of the enigmatic NSC terminal arbor onto long cytoplasmic processes engaging with and spreading over even remote blood vessels, a configuration reminiscent of early postnatal "juvenile" NSCs. Together, these findings suggest that VEGF preconditioning might be harnessed for long-term neurogenic enhancement despite continued exposure to an "aged" systemic milieu