43 research outputs found
On the Parisi-Toulouse hypothesis for the spin glass phase in mean-field theory
No full textWe consider the spin-glass phase of the Sherrington-Kirkpatrick model in the presence of a magnetic field. The series expansion of the Parisi function q(x) is computed at high orders in powers of τ= T C -T and H. We find that none of the Parisi-Toulouse scaling hypotheses on the q(x) behavior strictly holds, although some of them are violated only at high orders. The series is resummed yielding results in the whole spin-glass phase which are compared with those from a numerical evaluation of the q(x). At the high order considered, the transition turns out to be third order on the Almeida-Thouless line, a result which is confirmed rigorously computing the expansion of the solution near the line at finite τ. The transition becomes smoother for infinitesimally small field while it is third order at strictly zero field. © EDP Sciences, Società, Italiana di Fisica, Springer-Ver lag 2003
The Surveillance of T-Lymphocytes in the Human Blood Stream
No full textT-Lymphocytes (T-cells), one of the many different lymphocytes, are the precursors of disease detection. Their primary purpose is to maintain a healthy immune system. They use the blood vasculature (blood stream) and lymphatic system to circulate throughout the body. Study of a T-cells journey throughout the human blood stream is useful to understand how they can detect disease, such as cancer, in an efficient and effective manner. T-cells are to be thought of as the good cells in our body searching to destroy the bad cells (cancer/infectious cells). The thymus lies in the anterior mediastinum, which is directly behind the breast plate. Initially T-cells migrate from bone marrow to the thymus so that they may proliferate, mature, and become immunocompetent. Once immunocompetent they leave and journey throughout the body to help fight disease.
It is assumed that with a greater velocity in the blood stream, T-cells will circulate throughout the body much more efficiently. Hence, surveillance by faster T-cells will promote rapid detection of cancer cells. A steady-state 3-dimensional model has been coded to analyze and simulate the velocity of T-cells in the blood stream. This model is based upon the Newtonian properties of blood plasma. The mathematical properties of this model resemble those of the Navier-Stokes equation with some extra force terms added. These force terms are controlled by Beta and Gamma. Beta is the measure of an individuals quality of health. Gamma is the amount of stress an individual is exposed to. Depending on these variables, the velocity of Lymphocytes in the blood stream will vary. In an effort to achieve a steady-state model, a technique called Perturbed Functional Iterations (PFI) has been implemented
The perturbative structure of spin glass field theory
No full textAbstractCubic replicated field theory is used to study the glassy phase of the short-range Ising spin glass just below the transition temperature, and for systems above, at, and slightly below the upper critical dimension six. The order parameter function is computed up to two-loop order. There are two, well-separated bands in the mass spectrum, just as in mean field theory. The small mass band acts as an infrared cutoff, whereas contributions from the large mass region can be computed perturbatively (d>6), or interpreted by the ϵ-expansion around the critical fixed point (d=6−ϵ). The one-loop calculation of the (momentum-dependent) longitudinal mass, and the whole replicon sector is also presented. The innocuous behavior of the replicon masses while crossing the upper critical dimension shows that the ultrametric replica symmetry broken phase remains stable below six dimensions
Discrete stochastic geometry
No full textIn der vorliegenden Arbeit werden diverse Funktionale von Zufallspolytopen untersucht. Erwartungswerte des Volumens, der innerer Volumina, der Facettenzahl und des sogenannten T-Funktionals von Beta- und Beta'-Polytopen werden explizit ermittelt. Darüber hinaus wird die strikte Monotonie des Erwartungswerts der Facettenzahl bei wachsender Punktezahl gezeigt.
Es werden auch Zufallspolytope untersucht die von Zufallspunkten auf einer Halbsphäre erzeugt werden. Wir zeigen, dass der f-Vektor eines solchen Polytopes konvergiert, enge Zusammenhänge des f-Vektors zu Grassmannwinkeln und ermitteln das erste Glied der asymptotische Entwicklungen der Grassmannwinkel, wenn die Anzahl der Punkte gegen unendlich wächst. Darüber hinaus werden dazu assoziierte Poissonsche Punktprozesse untersucht.
Zuletzt wird das asymptotische Verhalten der maximalen Anzahl sogenannter "leere Simplizes" für eine Menge aus gleichverteilten Punkten aus einem konvexen Körper untersucht und bestimmt
The Gal/GalNAc lectin subunits are enriched on the surface of T-EhROM1-s cells.
No full textWildtype (WT) and T-EhROM1-s (ROM) cells were surface biotinylated. Labeled surface proteins were captured by avidin affinity chromatography. Both purified biotinylated surface proteins (hashed bars) and the unbound flow-through fraction, which represents intracellular protein (solid bars), were analyzed by SDS-PAGE and western blotting with antibodies specific for the heavy subunit (Hgl), the intermediate subunit (Igl) or the light subunit (Lgl). (A) Mean values of scanning densitometry data (n ≥ 3), reported as a percentage of total Hgl, Igl, or Lgl in WT cells, which was arbitrarily set to 100%. There is a statistically significant increase in the level of all three subunits on the surface of T-EhROM1-s amoebae (*PPP<0.05). (B) Representative western blots of intracellular (intracell) and surface proteins showing an increase in the level of Hgl, Igl and Lgl on the surface of mutant cells compared to that of wildtype cells. Actin, a cytosolic protein, serves as a control for premature cell breakage.</p
Renormalization group in spin glasses
No full textThe renormalization group treatment of spin glasses has been a theoretical challenge since shortly after the formulation of the Sherrington–Kirkpatrick model. This chapter brings three perspectives on this topic. Section 4.1, by T. Lubensky, reviews the early replica symmetric description of the problem, which predate and in some ways anticipate the discovery of the instability of that treatment by de Almeida and Thouless. The perturbative renormalization group approach to the ensuing transition is presented in Sec. 4.2, contributed jointly by T. Temesvari and I. Kondor. The findings of this approach motivate the consideration of non-perturbative renormalization group schemes, which are discussed in Sec. 4.3 written by M. C. Angelini. © 2023 by World Scientific Publishing Co. Pte. Ltd. All rights reserved
Stability of the Mézard-Parisi Solution for Random Manifolds
No full textThe eigenvalues of the Hessian associated with random manifolds are constructed for the general case of steps of replica symmetry breaking. For the Parisi limit (continuum replica symmetry breaking) which is relevant for the manifold dimension , they are shown to be non negative.Les valeurs propres de la hessienne, associée avec une variété aléatoire, sont construites dans le cas général de étapes de brisure de la symétrie des répliques. Dans la limite de Parisi, (brisure continue de la symétrie des répliques) qui est pertinente pour la dimension de la variété , on montre qu'elles sont non négatives
Dyson's equations for the (Ising) spin-glass
No full textA complex problem is solved here; we show how to write Dyson's equations for the (Ising)
spin-glass that relate the propagator to the mass operator . In other words we are
able to reduce the inversion of an ultrametric matrix to the solution of a Dyson's
equation in all sectors (for the replicon sector the result had already been derived). It
turns out that what renders the problem tractable is using, instead of the components of
(or ), an object called here the “kernel" from which one can deduce the components
themselves after dressing it with ultrametric weights and summing over eigenvalue indices
with their appropriate multiplicity. Dyson's equations are then established as stationarity
equations of tr In
, where the kinetic terms are incorporated in . At each
stage we illustrate the calculation by providing explicit answers for the bare system (meau
field in ). In particular the introduction of the “kernel" allows us to construct the
bare propagator for a Lagrangean where one retains all quartic invariants. The case of the
system in a magnetic field is also treated.Un problème complexe est résolu ici: nous établissons pour le verre de spin d'Ising, les
équations de Dyson qui relient le propagateur à l'opérateur de masse . En d'autres
termes nous réduisons l'inversion d'une matrice ultramétrique à la solution d'équations
de Dyson, et ceci dans tous les secteurs (ce résultat avait déjà été établi dans le secteur
du replicon). Ce qui rend ce problème abordable, c'est l'introduction en lieu et place des
composantes de (ou ), d'un objet appelé le “noyau" d'où les composantes pourront se
déduire après habillage ultramétrique et somme sur les indices de valeurs propres pondérées
par leur multiplicité. Les équations de Dyson sont alors établies comme équations de
stationnarité de tr In
, où les termes cinétiques sont incorporés dans . A
chaque étape, le calcul est illustré par le résultat explicite pour le système nu (champ
moyen pour ). En particulier l'introduction du “noyau" permet de construire les
propagateurs nus pour un lagrangien comportant tous les invariants quartiques. Enfin le
système en présence d'un champ magnétique est aussi résolu
