Algorithmic Boundedness-From-Below Conditions for Generic Scalar Potentials

Checking that a scalar potential is bounded from below (BFB) is an ubiquitous and notoriously difficult task in many models with extended scalar sectors. Exact analytic BFB conditions are known only in simple cases. In this work, we present a novel approach to algorithmically establish the BFB conditions for any polynomial scalar potential. The method relies on elements of multivariate algebra, in particular, on resultants and on the spectral theory of tensors, which is being developed by the mathematical community. We give first a pedagogical introduction to this approach, illustrate it with elementary examples, and then present the working Mathematica implementation publicly available at GitHub. Due to the rapidly increasing complexity of the problem, we have not yet produced ready-to-use analytical BFB conditions for new multi-scalar cases. But we are confident that the present implementation can be dramatically improved and may eventually lead to such results.Comment: 27 pages, 2 figures; v2: added reference

Algorithmic boundedness-from-below conditions for generic scalar potentials

Checking that a scalar potential is bounded from below (BFB) is an ubiquitous and notoriously difficult task in many models with extended scalar sectors. Exact analytic BFB conditions are known only in simple cases. In this work, we present a novel approach to algorithmically establish the BFB conditions for any polynomial scalar potential. The method relies on elements of multivariate algebra, in particular, on resultants and on the spectral theory of tensors, which is being developed by the mathematical community. We give first a pedagogical introduction to this approach, illustrate it with elementary examples, and then present the working Mathematica implementation publicly available at GitHub. Due to the rapidly increasing complexity of the problem, we have not yet produced ready-to-use analytical BFB conditions for new multi-scalar cases. But we are confident that the present implementation can be dramatically improved and may eventually lead to such results

Trigeminal neuralgia. Modern approach to classical percutaneous technique

Walton Centre for Neurology and Neurosurgery, Department of Neurosurgery, Liverpool, United Kingdom Spitalul Clinic de Urgenţă «Sf. Treime», Iaşi, RomaniaScopul acestei lucrări este de a prezenta termocoagularea percutana cu radiofrecvenţa transforamen oval ghidată de neuronavigaţie în tratamentul nevralgiei de trigemen esenţiale. Metode. Utilizarea neuronavigatiei în vederea localizării cu precizie maximă a foramenului oval a fost utilizată la 4 pacienţi cu nevralgie de trigemen în perioada 01.12.2006 – 30.04.2007. Toţi patru pacienţi au dezvoltat farmacorezistență la tratamentul medicamentos al nevralgiei de trigemen. Vârsta pacienţilor a fost între 62 și 78 ani. Rezultate. Neuronavigatia oferă o precizie crescută în timpul localizării foramenului oval în vederea termocoagulării cu radiofrecvența a ganglionului Gasser, ducând la sporirea confortului neurochirurgului în momentul atingerii țintei si reducerea riscului de posibile complicaţii ale acestei proceduri. Concluzii. Termocoagularea cu radiofrecvenţă percutană transforamen oval ghidată de neuronavigatie este o metodă sigură și promiţătoare pentru tratamentul nevralgiei de trigemen primare rezistent la medicamente, oferind controlul bun al durerii și reducerea riscului complicaţiilor existente în timpul «vânătorii» foramenului oval în metoda clasică. The objective of this work is to present preliminary results of neuronavigation-guided percutaneous radiofrequency thermocoagulation în the treatment of trigeminal neuralgia. Methods. Percutaneous radiofrequency thermocoagulation guided by neuronavigation was used în four patients with trigeminal neuralgia admitted to our hospital between 01.12.2006 and 30.04.2007. All patients developed pharmacoresistence to drugs used în the treatment of trigeminal or have had adverse effects due to drug toxicity. The age of the patients was between 62 and 78 years. Results. All the patients had an immediate pain relief after the percutaneous thermocoagulation guided by neuronavigation. în one case where, trigeminal neuralgia was secondary to petroclival meningioma the pain has recurrence shortly after the operation. Neuronavigation is a useful tool that gives to the neurosurgeon the comfort of direct visualization of instrument position în any time of the operation. It helps preoperative planning of the optimal trajectory for needle insertion and together with intraoperative stimulation provides an increased precision of foramen ovale targeting, reducing the risk of complication associated with this procedure. Conclusion. Percutaneous thermocoagulation guided by neuronavigationin the treatment of essential neuralgia is a safe and promising procedure. It gives a good pain control and reduce the risk of postoperative complications caused by hunting of foramen ovale.The objective of this work is to present preliminary results of neuronavigation-guided percutaneous radiofrequency thermocoagulation în the treatment of trigeminal neuralgia. Methods. Percutaneous radiofrequency thermocoagulation guided by neuronavigation was used în four patients with trigeminal neuralgia admitted to our hospital between 01.12.2006 and 30.04.2007. All patients developed pharmacoresistence to drugs used în the treatment of trigeminal or have had adverse effects due to drug toxicity. The age of the patients was between 62 and 78 years. Results. All the patients had an immediate pain relief after the percutaneous thermocoagulation guided by neuronavigation. în one case where, trigeminal neuralgia was secondary to petroclival meningioma the pain has recurrence shortly after the operation. Neuronavigation is a useful tool that gives to the neurosurgeon the comfort of direct visualization of instrument position în any time of the operation. It helps preoperative planning of the optimal trajectory for needle insertion and together with intraoperative stimulation provides an increased precision of foramen ovale targeting, reducing the risk of complication associated with this procedure. Conclusion. Percutaneous thermocoagulation guided by neuronavigationin the treatment of essential neuralgia is a safe and promising procedure. It gives a good pain control and reduce the risk of postoperative complications caused by hunting of foramen ovale

Computer guided techniques in intraoperative localization of brain lesions

Walton Centre for Neurology and Neurosurgery, Department of Neurosurgery, Liverpool, United Kingdom Spitalul Clinic de Urgenţă «Sf. Treime», Iaşi, RomaniaNeuronavigaţia şi stereotaxia sunt tehnici care vin în sprijinul neurochirurgului pentru a localiza cu un grad de precizie ridicat procesele expansive intracraniene şi structurile anatomice elocvente intracraniene. Chirurgia asistată de calculator s-a putut dezvolta doar în etapă, în care progresele tehnologice, şi în special cele în domeniul imagisticei şi informaticii au ajuns la un nivel foarte înalt. Principalele indicaţii ale neuronavigaţiei sunt reprezentate de localizarea cu precizie a unor leziuni intracerebrale profunde, de dimensiuni infracentimetrice, cu prezervarea concomitenta a structurilor cerebrale elocvente în vederea păstrării funcţionalităţii lor. Stereotaxia permite producerea de leziuni sau stimulări în nucleii gri centrali pentru tratamentul chirurgical al tulburărilor de mişcare rebele la tratamentul medicamentos. Aceste tehnici trebuie utilizate în majoritatea intervenţiilor neurochirurgicale pentru procese expansive intracraniene, aducând confort pentru pacient şi un plus de siguranţă pentru neurochirurg. În România acesta tehnologie a apărut din 2003, în patru centre neurochirurgicale. În articol sunt prezentate experienţa ultimilor cinci ani de utilizare a neuronavigaţiei împreună cu principiile şi tehnica operatorie.Neuronavigation and stereotaxy are techniques designed to help neurosurgeon to localize with a very high degree of precision different intracerebral pathological processes using a set of preoperative images (CT, MRI, fMRI, PET, SPECT etc.). The development of computer assisted surgery was possible only after a significant technological progress, especially in the area of informatics and imagistics. The main indications of neuronavigation are represented by targeting of small and deep intracerebral lesions and choosing the best way to approach them in order to preserve the neurological function. Stereotaxa allows also lesioning or stimulation of basal ganglia for treatment of movement disorders. These techniques can bring an important amount of confort both to the patient and to the neurosurgeon. In Romania neuronavigation was introduced in 2003 in four neurosurgical centers. We present our five-years experience in neuronavigation and describe the main principles and surgical technique

Fewer Mocks and Less Noise: Reducing the Dimensionality of Cosmological Observables with Subspace Projections

Creating accurate and low-noise covariance matrices represents a formidable challenge in modern-day cosmology. We present a formalism to compress arbitrary observables into a small number of bins by projection into a model-specific subspace that minimizes the prior-averaged log-likelihood error. The lower dimensionality leads to a dramatic reduction in covariance matrix noise, significantly reducing the number of mocks that need to be computed. Given a theory model, a set of priors, and a simple model of the covariance, our method works by using singular value decompositions to construct a basis for the observable that is close to Euclidean; by restricting to the first few basis vectors, we can capture almost all the constraining power in a lower-dimensional subspace. Unlike conventional approaches, the method can be tailored for specific analyses and captures non-linearities that are not present in the Fisher matrix, ensuring that the full likelihood can be reproduced. The procedure is validated with full-shape analyses of power spectra from BOSS DR12 mock catalogs, showing that the 96-bin power spectra can be replaced by 12 subspace coefficients without biasing the output cosmology; this allows for accurate parameter inference using only $\sim 100$ mocks. Such decompositions facilitate accurate testing of power spectrum covariances; for the largest BOSS data chunk, we find that: (a) analytic covariances provide accurate models (with or without trispectrum terms); and (b) using the sample covariance from the MultiDark-Patchy mocks incurs a $\sim 0.5\sigma$ shift in $\Omega_m$, unless the subspace projection is applied. The method is easily extended to higher order statistics; the $\sim 2000$-bin bispectrum can be compressed into only $\sim 10$ coefficients, allowing for accurate analyses using few mocks and without having to increase the bin sizes.Comment: 22 pages, 6 figures. Accepted by Phys. Rev.

Modeling Galaxies in Redshift Space at the Field Level

We develop an analytical forward model based on perturbation theory to predict the redshift-space galaxy overdensity at the field level given a realization of the initial conditions. We find that the residual noise between the model and simulated galaxy density has a power spectrum that is white on large scales, with size comparable to the shot noise. In the mildly nonlinear regime, we see a $k^2\mu^2$ correction to the noise power spectrum, corresponding to larger noise along the line of sight and on smaller scales. The parametric form of this correction has been predicted on theoretical grounds before, and our simulations provide important confirmation of its presence. We have also modeled the galaxy velocity at the field-level and compared it against simulated galaxy velocities, finding that about $10\%$ of the galaxies are responsible for half of the rms velocity residual for our simulated galaxy sample.Comment: 21 pages, 12 figures. Code available at https://github.com/mschmittfull/per

Quantification and modeling of macroparticle-induced mechanical stress for varying shake flask cultivation conditions

In biotechnological processes, filamentous microorganisms are known for their broad product spectrum and complex cellular morphology. Product formation and cellular morphology are often closely linked, requiring a well-defined level of mechanical stress to achieve high product concentrations. Macroparticles were added to shake flask cultures of the filamentous actinomycete Lentzea aerocolonigenes to find these optimal cultivation conditions. However, there is currently no model concept for the dependence of the strength and frequency of the bead-induced stress on the process parameters. Therefore, shake flask simulations were performed for combinations of bead size, bead concentration, bead density and shaking frequency. Contact analysis showed that the highest shear stresses were caused by bead-bottom contacts. Based on this, a newly generated characteristic parameter, the stress area ratio (SAR), was defined, which relates the bead wall shear and normal stresses to the total shear area. Comparison of the SAR with previous cultivation results revealed an optimum pattern for product concentration and mean product-to-biomass related yield coefficient. Thus, this model is a suitable tool for future optimization, comparison and scaling up of shear-sensitive microorganism cultivation. Finally, the simulation results were validated using high-speed recordings of the bead motion on the bottom of the shake flask

High frequency intrinsic modes in El Ni\~no Southern Oscillation Index

Recent $daily$ data of the Southern Oscillation Index have been analyzed. The power spectrum indicates major intrinsic geophysical short periods. We find interesting ``high frequency'' oscillations at 24, 27, 37, 76, 100 and 365 days. In particular the 24 days peaks may correspond to the Branstator-Kushnir wave, the 27 days may be due to the moon effect rotation, the 37 days peaks is most probably related to the Madden and Julian Oscillation. It is not yet clear the explanations for the 76 days which may be associated with interseasonal oscillation in the tropical atmosphere; the 100 days could be resulting from a mere beat between the 37 and 27 periods, or the 76 and 365 days. Next these periods are used to reconstruct the signal and to produce a forecast for the next 9 months, at the time of writing. After cleansing the signal of those periodicities a detrended fluctuation analysis is performed to reveal the nature of the stochastic structures in the signal and whether specific correlation can be found. We study the evolution of the distribution of first return times, in particular between $extreme$ $events$. A markedly significant difference from the expected distribution for uncorrelated events is found.Comment: accepted for publication on Physica