Uncertainty quantification for kinetic models in socio-economic and life sciences

Kinetic equations play a major rule in modeling large systems of interacting particles. Recently the legacy of classical kinetic theory found novel applications in socio-economic and life sciences, where processes characterized by large groups of agents exhibit spontaneous emergence of social structures. Well-known examples are the formation of clusters in opinion dynamics, the appearance of inequalities in wealth distributions, flocking and milling behaviors in swarming models, synchronization phenomena in biological systems and lane formation in pedestrian traffic. The construction of kinetic models describing the above processes, however, has to face the difficulty of the lack of fundamental principles since physical forces are replaced by empirical social forces. These empirical forces are typically constructed with the aim to reproduce qualitatively the observed system behaviors, like the emergence of social structures, and are at best known in terms of statistical information of the modeling parameters. For this reason the presence of random inputs characterizing the parameters uncertainty should be considered as an essential feature in the modeling process. In this survey we introduce several examples of such kinetic models, that are mathematically described by nonlinear Vlasov and Fokker--Planck equations, and present different numerical approaches for uncertainty quantification which preserve the main features of the kinetic solution.Comment: To appear in "Uncertainty Quantification for Hyperbolic and Kinetic Equations

The homotopy type of the loops on (n−1)(n-1)-connected (2n+1)(2n+1)-manifolds

For $n\geq 2$ we compute the homotopy groups of $(n-1)$-connected closed manifolds of dimension $(2n+1)$. Away from the finite set of primes dividing the order of the torsion subgroup in homology, the $p$-local homotopy groups of $M$ are determined by the rank of the free Abelian part of the homology. Moreover, we show that these $p$-local homotopy groups can be expressed as a direct sum of $p$-local homotopy groups of spheres. The integral homotopy type of the loop space is also computed and shown to depend only on the rank of the free Abelian part and the torsion subgroup.Comment: Trends in Algebraic Topology and Related Topics, Trends Math., Birkhauser/Springer, 2018. arXiv admin note: text overlap with arXiv:1510.0519

Cavity QED with a Bose-Einstein condensate

Cavity quantum electrodynamics (cavity QED) describes the coherent interaction between matter and an electromagnetic field confined within a resonator structure, and is providing a useful platform for developing concepts in quantum information processing. By using high-quality resonators, a strong coupling regime can be reached experimentally in which atoms coherently exchange a photon with a single light-field mode many times before dissipation sets in. This has led to fundamental studies with both microwave and optical resonators. To meet the challenges posed by quantum state engineering and quantum information processing, recent experiments have focused on laser cooling and trapping of atoms inside an optical cavity. However, the tremendous degree of control over atomic gases achieved with Bose-Einstein condensation has so far not been used for cavity QED. Here we achieve the strong coupling of a Bose-Einstein condensate to the quantized field of an ultrahigh-finesse optical cavity and present a measurement of its eigenenergy spectrum. This is a conceptually new regime of cavity QED, in which all atoms occupy a single mode of a matter-wave field and couple identically to the light field, sharing a single excitation. This opens possibilities ranging from quantum communication to a wealth of new phenomena that can be expected in the many-body physics of quantum gases with cavity-mediated interactions.Comment: 6 pages, 4 figures; version accepted for publication in Nature; updated Fig. 4; changed atom numbers due to new calibratio

Single-Atom Gating of Quantum State Superpositions

The ultimate miniaturization of electronic devices will likely require local and coherent control of single electronic wavefunctions. Wavefunctions exist within both physical real space and an abstract state space with a simple geometric interpretation: this state space--or Hilbert space--is spanned by mutually orthogonal state vectors corresponding to the quantized degrees of freedom of the real-space system. Measurement of superpositions is akin to accessing the direction of a vector in Hilbert space, determining an angle of rotation equivalent to quantum phase. Here we show that an individual atom inside a designed quantum corral can control this angle, producing arbitrary coherent superpositions of spatial quantum states. Using scanning tunnelling microscopy and nanostructures assembled atom-by-atom we demonstrate how single spins and quantum mirages can be harnessed to image the superposition of two electronic states. We also present a straightforward method to determine the atom path enacting phase rotations between any desired state vectors. A single atom thus becomes a real space handle for an abstract Hilbert space, providing a simple technique for coherent quantum state manipulation at the spatial limit of condensed matter.Comment: Published online 6 April 2008 in Nature Physics; 17 page manuscript (including 4 figures) + 3 page supplement (including 2 figures); supplementary movies available at http://mota.stanford.ed

Bang-bang control of fullerene qubits using ultra-fast phase gates

Quantum mechanics permits an entity, such as an atom, to exist in a superposition of multiple states simultaneously. Quantum information processing (QIP) harnesses this profound phenomenon to manipulate information in radically new ways. A fundamental challenge in all QIP technologies is the corruption of superposition in a quantum bit (qubit) through interaction with its environment. Quantum bang-bang control provides a solution by repeatedly applying `kicks' to a qubit, thus disrupting an environmental interaction. However, the speed and precision required for the kick operations has presented an obstacle to experimental realization. Here we demonstrate a phase gate of unprecedented speed on a nuclear spin qubit in a fullerene molecule (N@C60), and use it to bang-bang decouple the qubit from a strong environmental interaction. We can thus trap the qubit in closed cycles on the Bloch sphere, or lock it in a given state for an arbitrary period. Our procedure uses operations on a second qubit, an electron spin, in order to generate an arbitrary phase on the nuclear qubit. We anticipate the approach will be vital for QIP technologies, especially at the molecular scale where other strategies, such as electrode switching, are unfeasible

Plasma cholesterol levels and brain development in preterm newborns.

BackgroundTo assess whether postnatal plasma cholesterol levels are associated with microstructural and macrostructural regional brain development in preterm newborns.MethodsSixty preterm newborns (born 24-32 weeks gestational age) were assessed using MRI studies soon after birth and again at term-equivalent age. Blood samples were obtained within 7 days of each MRI scan to analyze for plasma cholesterol and lathosterol (a marker of endogenous cholesterol synthesis) levels. Outcomes were assessed at 3 years using the Bayley Scales of Infant Development, Third Edition.ResultsEarly plasma lathosterol levels were associated with increased axial and radial diffusivities and increased volume of the subcortical white matter. Early plasma cholesterol levels were associated with increased volume of the cerebellum. Early plasma lathosterol levels were associated with a 2-point decrease in motor scores at 3 years.ConclusionsHigher early endogenous cholesterol synthesis is associated with worse microstructural measures and larger volumes in the subcortical white matter that may signify regional edema and worse motor outcomes. Higher early cholesterol is associated with improved cerebellar volumes. Further work is needed to better understand how the balance of cholesterol supply and endogenous synthesis impacts preterm brain development, especially if these may be modifiable factors to improve outcomes

Experimental delayed-choice entanglement swapping

Motivated by the question, which kind of physical interactions and processes are needed for the production of quantum entanglement, Peres has put forward the radical idea of delayed-choice entanglement swapping. There, entanglement can be "produced a posteriori, after the entangled particles have been measured and may no longer exist". In this work we report the first realization of Peres' gedanken experiment. Using four photons, we can actively delay the choice of measurement-implemented via a high-speed tunable bipartite state analyzer and a quantum random number generator-on two of the photons into the time-like future of the registration of the other two photons. This effectively projects the two already registered photons onto one definite of two mutually exclusive quantum states in which either the photons are entangled (quantum correlations) or separable (classical correlations). This can also be viewed as "quantum steering into the past"

Pioglitazone Prevents Capillary Rarefaction in Streptozotocin-Diabetic Rats Independently of Glucose Control and Vascular Endothelial Growth Factor Expression

Background/Aims: Reduction of capillary network density occurs early in the development of metabolic syndrome and may be relevant for the precipitation of diabetes. Agonists of the peroxisome proliferator-activated receptor (PPAR)-gamma transcription factor are vasculoprotective, but their capacity for structural preservation of the microcirculation is unclear. Methods: Male Wistar rats were rendered diabetic by streptozotocin and treated with pioglitazone in chow for up to 12 weeks. Capillary density was determined in heart and skeletal muscle after platelet endothelial cell adhesion molecule-1 (PECAM-1) immunostaining. Hallmarks of apoptosis and angiogenesis were determined. Results: Capillary density deteriorated progressively in the presence of hyperglycemia (from 971/mm(2) to 475/mm(2) in quadriceps muscle during 13 weeks). Pioglitazone did not influence plasma glucose, left ventricular weight, or body weight but nearly doubled absolute and relative capillary densities compared to untreated controls (1.2 vs. 0.6 capillaries/myocyte in heart and 1.5 vs. 0.9 capillaries/myocyte in quadriceps muscle) after 13 weeks of diabetes. No antiapoptotic or angiogenic influence of pioglitazone was detected while a reduced expression of hypoxia-inducible factor-3 alpha and PPAR coactivator-1 alpha (PGC-1 alpha) mRNA as well as vascular endothelial growth factor (VEGF) protein possibly occurred as a consequence of improved vascularization. Conclusion: Pioglitazone preserves microvascular structure in diabetes independently of improvements in glycemic control and by a mechanism unrelated to VEGF-mediated angiogenesis. Copyright (C) 2012 S. Karger AG, Base

Mathematical Modelling of Optical Coherence Tomography

In this chapter a general mathematical model of Optical Coherence Tomography (OCT) is presented on the basis of the electromagnetic theory. OCT produces high resolution images of the inner structure of biological tissues. Images are obtained by measuring the time delay and the intensity of the backscattered light from the sample considering also the coherence properties of light. The scattering problem is considered for a weakly scattering medium located far enough from the detector. The inverse problem is to reconstruct the susceptibility of the medium given the measurements for different positions of the mirror. Different approaches are addressed depending on the different assumptions made about the optical properties of the sample. This procedure is applied to a full field OCT system and an extension to standard (time and frequency domain) OCT is briefly presented.Comment: 28 pages, 5 figures, book chapte