scholarly journals Permanental processes from products of complex and quaternionic induced Ginibre ensembles

2014 ◽  
Vol 03 (04) ◽  
pp. 1450014 ◽  
Author(s):  
Gernot Akemann ◽  
Jesper R. Ipsen ◽  
Eugene Strahov
Keyword(s):  
Large Fraction ◽  
Fixed Number ◽  
Leading Order ◽  
Asymptotic Results ◽  
Matrix Size ◽  
Ginibre Ensemble ◽  
Product Matrix ◽  
Finite Matrix ◽  
Complex Eigenvalues ◽  
Fixed Radius

We consider products of independent random matrices taken from the induced Ginibre ensemble with complex or quaternion elements. The joint densities for the complex eigenvalues of the product matrix can be written down exactly for a product of any fixed number of matrices and any finite matrix size. We show that the squared absolute values of the eigenvalues form a permanental process, generalizing the results of Kostlan and Rider for single matrices to products of complex and quaternionic matrices. Based on these findings, we can first write down exact results and asymptotic expansions for the so-called hole probabilities, that a disk centered at the origin is void of eigenvalues. Second, we compute the asymptotic expansion for the opposite problem, that a large fraction of complex eigenvalues occupies a disk of fixed radius centered at the origin; this is known as the overcrowding problem. While the expressions for finite matrix size depend on the parameters of the induced ensembles, the asymptotic results agree to leading order with previous results for products of square Ginibre matrices.

Non-Hermitian ensembles

2018 ◽  
Author(s):  
Alexei Morozov
Keyword(s):  
Random Matrix ◽  
Matrix Theory ◽  
Ginibre Ensemble ◽  
Fold Family ◽  
Large Matrix ◽  
Complex Eigenvalues ◽  
Wide Range ◽  
Random Matrix Ensembles ◽  
Matrix Ensembles ◽  
Physical Phenomena

This article discusses the three-fold family of Ginibre random matrix ensembles (complex, real, and quaternion real) and their elliptic deformations. It also considers eigenvalue correlations that are exactly reduced to two-point kernels in the strongly and weakly non-Hermitian limits of large matrix size. Ginibre introduced the complex, real, and quaternion real random matrix ensembles as a mathematical extension of Hermitian random matrix theory. Statistics of complex eigenvalues are now used in modelling a wide range of physical phenomena. After providing an overview of the complex Ginibre ensemble, the article describes random contractions and the complex elliptic ensemble. It then examines real and quaternion-real Ginibre ensembles, along with real and quaternion-real elliptic ensembles. In particular, it analyses the kernel in the elliptic case as well as the limits of strong and weak non-Hermiticity.

scholarly journals On the determinantal structure of conditional overlaps for the complex Ginibre ensemble

2019 ◽  
Vol 09 (04) ◽  
pp. 2050015 ◽  
Author(s):  
Gernot Akemann ◽  
Roger Tribe ◽  
Athanasios Tsareas ◽  
Oleg Zaboronski
Keyword(s):  
Scaling Limits ◽  
Algebraic Decay ◽  
Ginibre Ensemble ◽  
Complex Eigenvalues ◽  
The Matrix ◽  
Number Formula ◽  
Overlap Matrix ◽  
The Right ◽  
Joint Evolution ◽  
Eigenvectors And Eigenvalues

We continue the study of joint statistics of eigenvectors and eigenvalues initiated in the seminal papers of Chalker and Mehlig. The principal object of our investigation is the expectation of the matrix of overlaps between the left and the right eigenvectors for the complex [Formula: see text] Ginibre ensemble, conditional on an arbitrary number [Formula: see text] of complex eigenvalues. These objects provide the simplest generalization of the expectations of the diagonal overlap ([Formula: see text]) and the off-diagonal overlap ([Formula: see text]) considered originally by Chalker and Mehlig. They also appear naturally in the problem of joint evolution of eigenvectors and eigenvalues for Brownian motions with values in complex matrices studied by the Krakow school. We find that these expectations possess a determinantal structure, where the relevant kernels can be expressed in terms of certain orthogonal polynomials in the complex plane. Moreover, the kernels admit a rather tractable expression for all [Formula: see text]. This result enables a fairly straightforward calculation of the conditional expectation of the overlap matrix in the local bulk and edge scaling limits as well as the proof of the exact algebraic decay and asymptotic factorization of these expectations in the bulk.

scholarly journals The motion of a singular vortex near an escarpment

2001 ◽  
Vol 448 ◽  
pp. 335-365 ◽  
Author(s):  
D. C. DUNN ◽  
N. R. McDONALD ◽  
E. R. JOHNSON
Keyword(s):  
Linear Theory ◽  
Drift Velocity ◽  
Time Scale ◽  
Large Time ◽  
Wave Radiation ◽  
Moderate Intensity ◽  
Leading Order ◽  
Asymptotic Results ◽  
Contour Dynamics ◽  
Singular Vortex

McDonald (1998) has studied the motion of an intense, quasi-geostrophic, equivalent-barotropic, singular vortex near an infinitely long escarpment. The present work considers the remaining cases of the motion of weak and moderate intensity singular vortices near an escarpment. First, the limit that the vortex is weak is studied using linear theory. For times which are short compared to the advective time scale associated with the vortex it is found that topographic waves propagate rapidly away from the vortex and have no leading-order influence on the vortex drift velocity. The vortex propagates parallel to the escarpment in the sense of its image in the escarpment. The mechanism for this motion is identified and is named the pseudoimage of the vortex. Large-time asymptotic results predict that vortices which move in the same direction as the topographic waves radiate non-decaying waves and drift slowly towards the escarpment in response to wave radiation. Vortices which move in the opposite direction to the topographic waves reach a steadily propagating state. Contour dynamics results reinforce the linear theory in the limit that the vortex is weak, and show that the linear theory is less robust for vortices which move counter to the topographic waves. Second, contour dynamics results for a moderate intensity vortex are given. It is shown that dipole formation is a generic feature of the motion of moderate intensity vortices and induces enhanced motion in the direction perpendicular to the escarpment.

scholarly journals An Energy Budget for Signaling in the Grey Matter of the Brain

2001 ◽  
Vol 21 (10) ◽  
pp. 1133-1145 ◽  
Author(s):  
David Attwell ◽  
Simon B. Laughlin
Keyword(s):  
Action Potential ◽  
Grey Matter ◽  
Large Fraction ◽  
Fixed Number ◽  
Resting Potential ◽  
Energy Usage ◽  
Computing Power ◽  
Reduce Energy Consumption ◽  
The Brain ◽  
Physiologic Data

Anatomic and physiologic data are used to analyze the energy expenditure on different components of excitatory signaling in the grey matter of rodent brain. Action potentials and postsynaptic effects of glutamate are predicted to consume much of the energy (47% and 34%, respectively), with the resting potential consuming a smaller amount (13%), and glutamate recycling using only 3%. Energy usage depends strongly on action potential rate—an increase in activity of 1 action potential/cortical neuron/s will raise oxygen consumption by 145 mL/100 g grey matter/h. The energy expended on signaling is a large fraction of the total energy used by the brain; this favors the use of energy efficient neural codes and wiring patterns. Our estimates of energy usage predict the use of distributed codes, with ≤15% of neurons simultaneously active, to reduce energy consumption and allow greater computing power from a fixed number of neurons. Functional magnetic resonance imaging signals are likely to be dominated by changes in energy usage associated with synaptic currents and action potential propagation.

scholarly journals GUE-chGUE transition preserving chirality at finite matrix size

2018 ◽  
Vol 51 (34) ◽  
pp. 345202 ◽  
Author(s):  
Takuya Kanazawa ◽  
Mario Kieburg
Keyword(s):  
Matrix Size ◽  
Finite Matrix

Frequency Redistribution Effects in the Formation of Lyman α in Prominences and Their Influence on the Ratio of Hα to Lα

1979 ◽  
Vol 44 ◽  
pp. 53-55
Author(s):  
R.W. Milkey ◽  
J.N. Heasley ◽  
E.J. Schmahl ◽  
O. Engvold
Keyword(s):  
Line Profile ◽  
Large Fraction ◽  
Partial Frequency ◽  
Frequency Redistribution ◽  
Partial Frequency Redistribution ◽  
Emergent Intensity

The effect of partial frequency redistribution in the formation of Lyman α in the chromosphere has been discussed by Milkey and Mihalas (1973) and others, and it has been shown that in this case the coherency of scattering in the wings of the line substantially influences the line profile. Although there are non-negligible sources for La photons within a prominence, a large fraction of the emergent line photons are due to scattering of photons incident on the surface of the prominence so that one expects that in a prominence the frequency redistribution processes will play an important role in determining the emergent intensity.

Glucose metabolism in cancer cells: immunogold localization of hexokinase to the outer mitochondrial membrane

1995 ◽  
Vol 53 ◽  
pp. 1044-1045
Author(s):  
Krishan K. Arora ◽  
Glenn L. Decker ◽  
Peter L. Pedersen
Keyword(s):  
Tumor Cells ◽  
Mitochondrial Membrane ◽  
Present Report ◽  
Large Fraction ◽  
Mitochondrial Fraction ◽  
Immunogold Labeling ◽  
Outer Mitochondrial Membrane ◽  
Immunogold Localization ◽  
Hexokinase Activity ◽  
Normal Tissues

Hexokinase (ATP: D-hexose 6-phophotransferase EC 2.7.1.1) is the first enzyme of the glycolytic pathway which commits glucose to catabolism by catalyzing the phosphorylation of glucose with ATP. Previous studies have shown diat hexokinase activity is markedly elevated in rapidly growing tumor cells exhibiting high glucose catabolic rates. A large fraction (50-80%) of this enzyme activity is bound to the mitochondrial fraction (1,2) where it has preferred access to ATP (3). In contrast,the hexokinase activity of normal tissues is quite low, with one exception being brain which is a glucose-utilizing tissue (4). Biochemical evidence involving rigorous subfractionation studies have revealed striking differences between the subcellular distribution of hexokinase in normal and tumor cells [See review by Arora et al (4)].In the present report, we have utilized immunogold labeling techniques to evaluate die subcellular localization of hexokinase in highly glycolytic AS-30D hepatoma cells and in the tissue of its origin, i.e., rat liver.

Interactive multiobjective DEA target setting using lexicographic DDF

2020 ◽  
Vol 54 (6) ◽  
pp. 1703-1722 ◽  
Author(s):  
Narges Soltani ◽  
Sebastián Lozano
Keyword(s):  
Efficient Frontier ◽  
Directional Distance Function ◽  
Fixed Number ◽  
Optimization Approach ◽  
Target Setting ◽  
Interactive Process ◽  
Decision Making Unit ◽  
Setting Approach ◽  
Promising Area ◽  
Current Region

In this paper, a new interactive multiobjective target setting approach based on lexicographic directional distance function (DDF) method is proposed. Lexicographic DDF computes efficient targets along a specified directional vector. The interactive multiobjective optimization approach consists in several iteration cycles in each of which the Decision Making Unit (DMU) is presented a fixed number of efficient targets computed corresponding to different directional vectors. If the DMU finds one of them promising, the directional vectors tried in the next iteration are generated close to the promising one, thus focusing the exploration of the efficient frontier on the promising area. In any iteration the DMU may choose to finish the exploration of the current region and restart the process to probe a new region. The interactive process ends when the DMU finds its most preferred solution (MPS).

Phospholipid-Protein Interactions in the Formation of Prothrombin Activator

1965 ◽  
Vol 14 (03/04) ◽  
pp. 431-444 ◽  
Author(s):  
E. R Cole ◽  
J. L Koppel ◽  
J. H Olwin
Keyword(s):  
Complex Formation ◽  
Protein Interactions ◽  
Calcium Ions ◽  
Fixed Number ◽  
Factor V ◽  
Clotting Factors ◽  
Number Of Binding Sites ◽  
C Complex ◽  
Autoprothrombin C

SummarySince Ac-globulin (factor V) is involved in the formation of prothrombin activator, its ability to complex with phospholipids was studied. Purified bovine Ac-globulin was complexed to asolectin, there being presumably a fixed number of binding sites on the phospholipid micelle for Ac-globulin. In contrast to the requirement for calcium ions in the formation of complexes between asolectin and autoprothrombin C, calcium ions were not required for complex formation between asolectin and Ac-globulin to occur ; in fact, the presence of calcium prevented complex formation occurring, the degree of inhibition being dependent on the calcium concentration. By treating isolated, pre-formed aso- lectin-Ac-globulin complexes with calcium chloride solutions, Ac-globulin could be recovered in a much higher state of purity and essentially free of asolectin.Complete activators were formed by first preparing the asolectin-calcium- autoprothrombin C complex and then reacting the complex with Ac-globulin. A small amount of this product was very effective as an activator of purified prothrombin without further addition of calcium or any other cofactor. If the autoprothrombin C preparation used to prepare the complex was free of traces of prothrombin, the complete activator was stable for several hours at room temperature. Stable preparations of the complete activator were centrifuged, resulting in the sedimentation of most of the activity. Experimental evidence also indicated that activator activity was highest when autoprothrombin C and Ac-globulin were complexed to the same phospholipid micelle, rather than when the two clotting factors were complexed to separate micelles. These data suggested that the in vivo prothrombin activator may be a sedimentable complex composed of a thromboplastic enzyme, calcium, Ac-globulin and phospholipid.

IN SITU AND PILOT ORGAN PERFUSION TECHNIQUES FOR THE STUDY OF METABOLIC DYNAMICS

1972 ◽  
Vol 68 (2_Supplb) ◽  
pp. S9-S25 ◽  
Author(s):  
John Urquhart ◽  
Nancy Keller
Keyword(s):  
Cardiac Output ◽  
Large Fraction ◽  
Experimental Studies ◽  
Test Substance ◽  
Organ Perfusion ◽  
Systemic Blood ◽  
Experimental Control ◽  
Arterial Blood ◽  
Vascular Connections

ABSTRACT Two techniques for organ perfusion with blood are described which provide a basis for exploring metabolic or endocrine dynamics. The technique of in situ perfusion with autogenous arterial blood is suitable for glands or small organs which receive a small fraction of the animal's cardiac output; thus, test stimulatory or inhibitory substances can be added to the perfusing blood and undergo sufficient dilution in systemic blood after passage through the perfused organ so that recirculation does not compromise experimental control over test substance concentration in the perfusate. Experimental studies with the in situ perfused adrenal are described. The second technique, termed the pilot organ method, is suitable for organs which receive a large fraction of the cardiac output, such as the liver. Vascular connections are made between the circulation of an intact, anaesthetized large (> 30 kg) dog and the liver of a small (< 3 kg) dog. The small dog's liver (pilot liver) is excised and floated in a bath of canine ascites, and its venous effluent is continuously returned to the large dog. Test substances are infused into either the hepatic artery or portal vein of the pilot liver, but the small size of the pilot liver and its blood flow in relation to the large dog minimize recirculation effects. A number of functional parameters of the pilot liver are described.

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