There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Normal tissue cells are generally not viable when suspended in a fluid and are therefore said to be anchorage dependent. Such cells must adhere to a solid, but a solid can be as rigid as glass or softer than a baby's skin. The behavior of some cells on soft materials is characteristic of important phenotypes; for example, cell growth on soft agar gels is used to identify cancer cells. However, an understanding of how tissue cells-including fibroblasts, myocytes, neurons, and other cell types-sense matrix stiffness is just emerging with quantitative studies of cells adhering to gels (or to other cells) with which elasticity can be tuned to approximate that of tissues. Key roles in molecular pathways are played by adhesion complexes and the actinmyosin cytoskeleton, whose contractile forces are transmitted through transcellular structures. The feedback of local matrix stiffness on cell state likely has important implications for development, differentiation, disease, and regeneration.

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Tissue Cells Feel and Respond to the Stiffness of Their Substrate

Cell migration is a highly integrated multistep process that orchestrates embryonic morphogenesis; contributes to tissue repair and regeneration; and drives disease progression in cancer, mental retardation, atherosclerosis, and arthritis. The migrating cell is highly polarized with complex regulatory pathways that spatially and temporally integrate its component processes. This review describes the mechanisms underlying the major steps of migration and the signaling pathways that regulate them, and outlines recent advances investigating the nature of polarity in migrating cells and the pathways that establish it.

/pdf/cell-migration-integrating-signals-from-front-to-back-g0h3q2xs5i.pdf

Cell migration: integrating signals from front to back.

Topological quantum computation has emerged as one of the most exciting approaches to constructing a fault-tolerant quantum computer. The proposal relies on the existence of topological states of matter whose quasiparticle excitations are neither bosons nor fermions, but are particles known as non-Abelian anyons, meaning that they obey non-Abelian braiding statistics. Quantum information is stored in states with multiple quasiparticles, which have a topological degeneracy. The unitary gate operations that are necessary for quantum computation are carried out by braiding quasiparticles and then measuring the multiquasiparticle states. The fault tolerance of a topological quantum computer arises from the nonlocal encoding of the quasiparticle states, which makes them immune to errors caused by local perturbations. To date, the only such topological states thought to have been found in nature are fractional quantum Hall states, most prominently the $\ensuremath{\nu}=5∕2$ state, although several other prospective candidates have been proposed in systems as disparate as ultracold atoms in optical lattices and thin-film superconductors. In this review article, current research in this field is described, focusing on the general theoretical concepts of non-Abelian statistics as it relates to topological quantum computation, on understanding non-Abelian quantum Hall states, on proposed experiments to detect non-Abelian anyons, and on proposed architectures for a topological quantum computer. Both the mathematical underpinnings of topological quantum computation and the physics of the subject are addressed, using the $\ensuremath{\nu}=5∕2$ fractional quantum Hall state as the archetype of a non-Abelian topological state enabling fault-tolerant quantum computation.

Non-Abelian Anyons and Topological Quantum Computation

REVIEW Semiconductor devices generally take advantage of the charge of electrons, whereas magnetic materials are used for recording information involving electron spin. To make use of both charge and spin of electrons in semiconductors, a high concentration of magnetic elements can be introduced in nonmagnetic III-V semiconductors currently in use for devices. Low solubility of magnetic elements was overcome by low-temperature nonequilibrium molecular beam epitaxial growth, and ferromagnetic (Ga,Mn)As was realized. Magnetotransport measurements revealed that the magnetic transition temperature can be as high as 110 kelvin. The origin of the ferromagnetic interaction is discussed. Multilayer heterostructures including resonant tunneling diodes (RTDs) have also successfully been fabricated. The magnetic coupling between two ferromagnetic (Ga,Mn)As films separated by a nonmagnetic layer indicated the critical role of the holes in the magnetic coupling. The magnetic coupling in all semiconductor ferromagnetic/nonmagnetic layered structures, together with the possibility of spin filtering in RTDs, shows the potential of the present material system for exploring new physics and for developing new functionality toward future electronics.

https://science.sciencemag.org/content/sci/281/5379/951.full.pdf

Making Nonmagnetic Semiconductors Ferromagnetic

Mechanical forces play a major role in the regulation of cell adhesion and cytoskeletal organization. In order to explore the molecular mechanism underlying this regulation, we have investigated the relationship between local force applied by the cell to the substrate and the assembly of focal adhesions. A novel approach was developed for real-time, high-resolution measurements of forces applied by cells at single adhesion sites. This method combines micropatterning of elastomer substrates and fluorescence imaging of focal adhesions in live cells expressing GFPtagged vinculin. Local forces are correlated with the orientation, total fluorescence intensity and area of the focal adhesions, indicating a constant stress of 5.5 ± 2 nNμm-2. The dynamics of the force-dependent modulation of focal adhesions were characterized by blocking actomyosin contractility and were found to be on a time scale of seconds. The results put clear constraints on the possible molecular mechanisms for the mechanosensory response of focal adhesions to applied force.

Force and focal adhesion assembly: a close relationship studied using elastic micropatterned substrates

How localized electrons interact with delocalized electrons is a central question to many problems in sold-state physics1,2,3. The simplest manifestation of this situation is the Kondo effect, which occurs when an impurity atom with an unpaired electron is placed in a metal2. At low temperatures a spin singlet state is formed between the unpaired localized electron and delocalized electrons at the Fermi energy. Theories predict4,5,6,7 that a Kondo singlet should form in a single-electron transistor (SET), which contains a confined ‘droplet’ of electrons coupled by quantum-mechanical tunnelling to the delocalized electrons in the transistor's leads. If this is so, a SET could provide a means of investigating aspects of the Kondo effect under controlled circumstances that are not accessible in conventional systems: the number of electrons can be changed from odd to even, the difference in energy between the localized state and the Fermi level can be tuned, the coupling to the leads can be adjusted, voltage differences can be applied to reveal non-equilibrium Kondo phenomena7, and a single localized state can be studied rather than a statistical distribution. But for SETs fabricated previously, the binding energy of the spin singlet has been too small to observe Kondo phenomena. Ralph and Buhrman8 have observed the Kondo singlet at a single accidental impurity in a metal point contact, but with only two electrodes and without control over the structure they were not able to observe all of the features predicted. Here we report measurements on SETs smaller than those made previously, which exhibit all of the predicted aspects of the Kondo effect in such a system.

Kondo effect in a single-electron transistor

The question of how localized electrons interact with delocalized electrons is central to many problems at the forefront of solid state physics. The simplest example is the Kondo phenomenon, which occurs when an impurity atom with an unpaired electron is placed in a metal, and the energy of the unpaired electron is far below the Fermi energy. At low temperatures a spin singlet state is formed between the unpaired localized electron and delocalized electrons at the Fermi energy. 
The confined droplet of electrons interacting with the leads of a single electron transistor (SET) is closely analogous to an impurity atom interacting with the delocalized electrons in a metal. (Meir, Wingreen and Lee, 1993) We report here measurements on a new generation of SETs that display all the aspects of the Kondo phenomenon: the spin singlet forms and causes an enhancement of the zero-bias conductance when the number of electrons on the artificial atom is odd but not when it is even. The singlet is altered by applying a voltage or magnetic field or by increasing the temperature, all in ways that agree with predictions. (Wingreen and Meir 1994)

https://arxiv.org/pdf/cond-mat/9707311.pdf

Kondo Physics in a Single Electron Transistor

Since Millikan's famous oil-drop experiments1, it has been well known that electrical charge is quantized in units of the charge of an electron, e. For this reason, the theoretical prediction2,3 by Laughlin of the existence of fractionally charged ‘quasiparticles’—proposed as an explanation for the fractional quantum Hall (FQH) effect—is very counterintuitive. The FQH effect is a phenomenon observed in the conduction properties of a two-dimensional electron gas subjected to a strong perpendicular magnetic field. This effect results from the strong interaction between electrons, brought about by the magnetic field, giving rise to the aforementioned fractionally charged quasiparticles which carry the current. Here we report the direct observation of these counterintuitive entities by using measurements of quantum shot noise. Quantum shot noise results from the discreteness of the current-carrying charges and so is proportional to both the charge of the quasiparticles and the average current. Our measurements of quantum shot noise show unambiguously that current in a two-dimensional electron gas in the FQH regime is carried by fractional charges—e/3 in the present case—in agreement with Laughlin's prediction.

Direct observation of a fractional charge

We demonstrate that the conductance through a single-electron transistor at low temperature is in quantitative agreement with predictions of the equilibrium Anderson model. The Kondo effect is observed when an unpaired electron is localized within the transistor. Tuning the unpaired electron's energy toward the Fermi level in nearby leads produces a crossover between the Kondo and mixed-valence regimes of the Anderson model.

Diana Mahalu

Papers

Force and focal adhesion assembly: a close relationship studied using elastic micropatterned substrates

Kondo effect in a single-electron transistor

Kondo Physics in a Single Electron Transistor

Direct observation of a fractional charge

From the Kondo Regime to the Mixed-Valence Regime in a Single-Electron Transistor