Proof of the cases p≤7p \leq 7 of the Lieb-Seiringer formulation of the Bessis-Moussa-Villani conjecture

It is shown that the polynomial $\lambda(t) = {\rm Tr}[(A + tB)^p]$ has nonnegative coefficients when $p \leq 7$ and A and B are any two complex positive semidefinite $n \times n$ matrices with arbitrary $n$. This proofs a general nontrivial case of the Lieb-Seiringer formulation of the Bessis-Moussa-Villani conjecture which is a long standing problem in theoretical physics.Comment: 5 pages; typos corrected; accepted for publication in Journal of Statistical Physic

A novel FoxD3 gene trap line reveals neural crest precursor movement and a role for FoxD3 in their specification

Neural crest cells migrate extensively and contribute to diverse derivatives, including the craniofacial skeleton, peripheral neurons and glia, and pigment cells. Although several transgenic lines label neural crest subpopulations, few are suited for studying early events in neural crest development. Here, we present a zebrafish gene/protein trap line gt(foxd3-citrine)^(ct110a) that expresses a Citrine fusion protein with FoxD3, a transcription factor expressed in premigratory and migrating neural crest cells. In this novel line, citrine expression exactly parallels endogenous foxd3 expression. High-resolution time-lapse imaging reveals the dynamic phases of precursor and migratory neural crest cell movements from the neural keel stage to times of active cell migration. In addition, Cre-recombination produces a variant line FoxD3-mCherry-pA whose homozygosis generates a FoxD3 mutant. Taking advantage of the endogenously regulated expression of FoxD3-mCherry fusion protein, we directly assess early effects of FoxD3 loss-of-function on specification and morphogenesis of dorsal root ganglia, craniofacial skeleton and melanophores. These novel lines provide new insights and useful new tools for studying specification, migration and differentiation of neural crest cells

On the intrinsic complexity of the arithmetic Nullstellensatz

We show several arithmetic estimates for Hilbert's Nullstellensatz. This includes an algorithmic procedure computing the polynomials and constants occurring in a Bézout identity, whose complexity is polynomial in the geometric degree of the system. Moreover, we show for the first time height estimates of intrinsic type for the polynomials and constants appearing, again polynomial in the geometric degree and linear in the height of the system. These results are based on a suitable representation of polynomials by straight-line programs and duality techniques using the Trace Formula for Gorenstein algebras. As an application we show more precise upper bounds for the function πS(x) counting the number of primes yielding an inconsistent modular polynomial equation system. We also give a computationally interesting lower bound for the density of small prime numbers of controlled bit length for the reduction to positive characteristic of inconsistent systems. Again, this bound is given in terms of intrinsic parameters.Facultad de Ciencias Exacta

Zebrafish Stem/Progenitor Factor msi2b Exhibits Two Phases of Activity Mediated by Different Splice Variants

The Musashi (Msi) family of RNA-binding proteins is important in stem and differentiating cells in many species. Here, we present a zebrafish gene/protein trap line gt(msi2b-citrine)(ct) (57) (a) that expresses a Citrine fusion protein with endogenous Msi2b. Our results reveal two phases of Msi2b expression: ubiquitous expression in progenitor cells in the early embryo and later, tissue-specific expression in differentiating cells in the olfactory organ, pineal gland, and subpopulations of neurons in the central nervous system (CNS). Interestingly, this division between early and late phases is paralleled by differential expression of msi2b alternative splicing products. Whereas the full-length and long variant v3 Msi2b predominate at early stages, the later expression of variants in differentiating tissues appears to be tissue specific. Using the gt(msi2b-citrine)(ct) (57) (a), we characterized tissue-specific expression of Msi2b with cellular resolution in subsets of differentiating cells in the olfactory organ, pineal gland, CNS, and ventral neural tube. By performing transcription activator-like effectors nuclease-mediated biallelic genome editing or morpholino knockdown of Msi2b in zebrafish, our results show that early inactivation of Msi2b results in severe embryonic defects including hypertrophy of the ventricles and shortening of the body, consistent with an important role in cell proliferation and survival. Moreover, specific inactivation of Msi2b full-length indicates that this species is essential for the early role of Msi2b. This line provides a valuable tool both for live imaging of the endogenous Msi2b at subcellular resolution and manipulation of Msi2b-expressing cells

On the intrinsic complexity of the arithmetic Nullstellensatz

We show several arithmetic estimates for Hilbert's Nullstellensatz. This includes an algorithmic procedure computing the polynomials and constants occurring in a Bézout identity, whose complexity is polynomial in the geometric degree of the system. Moreover, we show for the first time height estimates of intrinsic type for the polynomials and constants appearing, again polynomial in the geometric degree and linear in the height of the system. These results are based on a suitable representation of polynomials by straight-line programs and duality techniques using the Trace Formula for Gorenstein algebras. As an application we show more precise upper bounds for the function πS(x) counting the number of primes yielding an inconsistent modular polynomial equation system. We also give a computationally interesting lower bound for the density of small prime numbers of controlled bit length for the reduction to positive characteristic of inconsistent systems. Again, this bound is given in terms of intrinsic parameters.Facultad de Ciencias Exacta

The temperature and ionization structure of the emitting gas in HII galaxies: Implications for the accuracy of abundance determinations

We propose a methodology to perform a self-consistent analysis of the physical properties of the emitting gas of HII galaxies adequate to the data that can be obtained with the XXI century technology. This methodology requires the production and calibration of empirical relations between the different line temperatures that should superseed currently used ones based on very simple, and poorly tested, photo-ionization model sequences. As a first step to reach these goals we have obtained simultaneous blue to far red longslit spectra with the William Herschel Telescope (WHT) of three compact HII galaxies selected from the Sloan Digital Sky Survey (SDSS) Data Release 2 (DR2) spectral catalog using the INAOE Virtual Observatory superserver. Our spectra cover the range from 3200 to 10500 \AA, including the Balmer jump, the [OII]3727,29 \AA lines, the [SIII]9069,9532 \AA doublet as well as various weak auroral lines such as [OIII]4363 \AA and [SIII]6312 \AA. For the three objects we have measured at least four line temperatures: T([OIII]), T([SIII]), T([OII]) and T([SII]) and the Balmer continuum temperature T(Bac). These measurements and a careful and realistic treatment of the observational errors yield total oxygen abundances with accuracies between 5 and 9%. These accuracies are expected to improve as better calibrations based on more precise measurements, both on electron temperatures and densities, are produced. ..

Kinematics of metal-rich circumnuclear regions from future 8-m class observations

This is an electronic version of an article published in Revista Mexicana de Astronomía y Astrofísica. Terlevich, E. et al. Kinematics of metal-rich circumnuclear regions from future 8-m class observations. Revista Mexicana de Astronomía y Astrofísica 29 (2007): 16

Laminin β1a controls distinct steps during the establishment of digestive organ laterality

Visceral organs, including the liver and pancreas, adopt asymmetric positions to ensure proper function. Yet the molecular and cellular mechanisms controlling organ laterality are not well understood. We identified a mutation affecting zebrafish laminin β1a (lamb1a) that disrupts left-right asymmetry of the liver and pancreas. In these mutants, the liver spans the midline and the ventral pancreatic bud remains split into bilateral structures. We show that lamb1a regulates asymmetric left-right gene expression in the lateral plate mesoderm (LPM). In particular, lamb1a functions in Kupffer’s vesicle (KV), a ciliated organ analogous to the mouse node, to control the length and function of the KV cilia. Later during gut-looping stages, dynamic expression of Lamb1a is required for the bilayered organization and asymmetric migration of the LPM. Loss of Lamb1a function also results in aberrant protrusion of LPM cells into the gut. Collectively, our results provide cellular and molecular mechanisms by which extracellular matrix proteins regulate left-right organ morphogenesis

Physical parameters in circumnuclear star forming regions

This is an electronic version of an article published in Revista Mexicana de Astronomía y Astrofísica. Hägele, G.E. et al. Physical parameters in circumnuclear star forming regions. Revista Mexicana de Astronomía y Astrofísica 33 (2008): 17