Variational wave functions, ground state and their overlap

An intrinsic measure of the quality of a variational wave function is given by its overlap with the ground state of the system. We derive a general formula to compute this overlap when quantum dynamics in imaginary time is accessible. The overlap is simply related to the area under the $E(\tau)$ curve, i.e. the energy as a function of imaginary time. This has important applications to, for example, quantum Monte-Carlo algorithms where the overlap becomes as a simple byproduct of routine simulations. As a result, we find that the practical definition of a good variational wave function for quantum Monte-Carlo simulations, {\it i.e.} fast convergence to the ground state, is equivalent to a good overlap with the actual ground state of the system.Comment: 4 pages, 2 figures, to be published in Phys. Rev. Lett. (revised version

Navier-Stokes equations : unpredictability even without butterfiles?

Mathematically, the motion of a fluid is described by the so-called Navier-Stokes equations. In the spirit of Newtonian mechanics, these equations should determine the future motion of the fluid out of its initial state. However, despite the significant effort made for more than a century, this determinism has not yet been mathematically proved nor disproved. This paper offers a general perspective on the Navier-Stokes equations, the fourth millennium problem

Votar : no tan fàcil com sembla, però podríem fer-ho millor!

Aquest article té un doble objectiu. D'una banda, volem fer veure com efectivament el problema no és pas una trivialitat, sinó que té molt de sentit adoptar un punt de vista matemàtic, amb definicions precises i demostracions rigoroses. D'altra banda, també volem incidir en les implicacions pràctiques d'aquesta anàlisi. En particular, veurem com els mètodes de votació més senzills tenen defectes importants que podrien ser corregits mitjançant la utilització d'altres mètodes més elaborats

Sobre la figura d'unamà trobada com a ornamentació en les recents excavacions arqueològiques del castell de Tartareu

S'identifica el llinatge al que correspondria una certa figura de caràcter heràldic que apareix com a ornamentació en les recents excavacions arqueològiques del castell de Tartare

Les equacions de Navier-Stokes. Un repte al determinisme Newtonià

S'examina la qüestió de l'existència i unicitat de solució de les equacions de Navier-Stokes no estacionàries. Es posa especial èmfasi en les implicacions filosòfiques i la perspectiva històrica. L'exposició pretén acostar-se al nucli del problema tot mantenint un llenguatge al menys tècnic possible

Eleccions mitjançant el vot d'aprovació. El mètode de Phragmén i algunes variants

S'estudien diverses variants d'un mètode de representació proporcional que Edvard Phragmén va proposar a finals del segle xix. Cada elector expressa la seva opinió mitjançant un vot d'aprovació, on indica totes les opcions que li semblen adients. Les opcions poden ser candidats individuals, com suposava Phragmén, o bé candidatures de partit que ofereixen múltiples representants cadascuna. Donat un conjunt de vots d'aquest tipus i un nombre prefixat d'escons, es tracta de repartir aquests escons entre les diferents candidatures de manera que el resultat sigui el més representatiu possible. El present estudi presta una atenció especial a una propietat de monotonia que demana que l'addició d'aprovacions a favor d'una candidatura no pugui produir una disminució del nombre d'escons que li són assignats. En la variant bàsica, on els escons s'assignen mitjançant un procediment seqüencial, aquesta monotonia es compleix en el cas de candidats individuals, però no en el cas de candidatures de partit. També s'exploren breument unes variants directes, on els escons s'assignen tots d'una vegada mitjançant algun criteri adient d'optimització. Aquestes variants semblen millors des del punt de vista de la monotonia, però presenten un problema de multiplicitat de solucions que fa necessari algun criteri addicional de selecció.We study certain variants of a method for proportional representation that was proposed at the end of the nineteenth century by Edvard Phragmén. Every elector expresses his opinion by means of an approval ballot, where he indicates all the options that he deems suitable. The options can be individual candidates, as it was considered by Phragmén, or party candidatures which can provide several representatives each. Given a set of votes of this kind and a prefixed number of seats, the aim is to distribute these seats among the candidatures so as to achieve as much representativeness as possible. This work pays special attention to a condition of monotonicity which requires that adding approvals in favour of a certain candidature cannot result in its getting a smaller number of seats. In the basic variant, where seats are assigned by means of a sequential procedure, such a monotonicity holds in the case of individual candidates but not in the general case. We briefly explore also some direct variants, where seats are assigned all at once by means of a suitable optimization criterion. These variants seem to be better from the point of view of monotonicity. However, they suffer from a problem of multiplicity of solutions that calls for a supplementary criterion to choose among them

Neurobehavioral and Gene Expression Effects of Early Embryonic Methylmercury Exposure in Yellow Perch (Perca flavescens) and Zebrafish (Danio rerio) Larvae

Methylmercury (MeHg) is a pervasive and persistent neurotoxic environmental pollutant known to affect the behavior of fish, birds and mammals. The present study addresses the neurobehavioral and gene expression effects of MeHg in yellow perch (Perca flavescens) and zebrafish (Danio rerio) embryos. The rationale for this study originated from an interest to understand the behavioral and molecular phenotypes of environmental MeHg exposure in the yellow perch, an ecologically and economically relevant species of the North American Great Lakes region. Both MeHg and the yellow perch coexist in a common ecosystem: the North American Great Lakes. However, the effects of this organism-contaminant interaction are poorly understood. The zebrafish was utilized here as a surrogate model for yellow perch, due to its ease of rearing, whole sequenced genome and its status as an NIH endorsed model organism. The objectives of this study were to understand the effects of MeHg on behaviors that are critical for survival both in yellow perch and zebrafish. Among the behavioral paradigms tested, this study addressed fundamental behaviors for the survival of young larval fish, namely swimming and prey capture. Furthermore, this study screened for gene expression alterations in the same cohorts of fish for which behavioral analysis was performed; this was done to gain insight into the gene pathways involved in MeHg-induced neurotoxicity, as well as to expand the knowledge about biomarkers of MeHg exposure in the yellow perch. Here, we have uncovered important differences and similarities between the effects of MeHg exposure in yellow perch and zebrafish larvae, both in terms of behavioral and molecular responses to MeHg. The findings of this study suggest that environmentally relevant MeHg exposure can adversely affect the behavior of yellow perch larvae and impair fundamental survival skills. Furthermore, this study determined that although it would be challenging to relate behavioral endpoints between yellow perch and zebrafish, molecular responses between these two species could be more conserved