Minimal Length Uncertainty Relations and New Shape Invariant Models

This paper identifies a new class of shape invariant models. These models are based on extensions of conventional quantum mechanics that satisfy a string-motivated minimal length uncertainty relation. An important feature of our construction is the pairing of operators that are not adjoints of each other. The results in this paper thus show the broader applicability of shape invariance to exactly solvable systems.Comment: 11 pages, no figure

Duality and Central Charges in Supersymmetric Quantum Mechanics

We identify a class of point-particle models that exhibit a target-space duality. This duality arises from a construction based on supersymmetric quantum mechanics with a non-vanishing central charge. Motivated by analogies to string theory, we are led to speculate regarding mechanisms for restricting the background geometry.Comment: 10 pages, 1 figure, late

Applications of Partial Supersymmetry

I examine quantum mechanical Hamiltonians with partial supersymmetry, and explore two main applications. First, I analyze a theory with a logarithmic spectrum, and show how to use partial supersymmetry to reveal the underlying structure of this theory. This method reveals an intriguing equivalence between two formulations of this theory, one of which is one-dimensional, and the other of which is infinite-dimensional. Second, I demonstrate the use of partial supersymmetry as a tool to obtain the asymptotic energy levels in non-relativistic quantum mechanics in an exceptionally easy way. In the end, I discuss possible extensions of this work, including the possible connections between partial supersymmetry and renormalization group arguments.Comment: 11 pages, harvmac, no figures; typo corrected in identifying info on title pag

The dynamics of chromosome organization and gene regulation

With the sequence of the human genome now complete, studies must focus on how the genome is functionally organized within the confines of the cell nucleus and the dynamic interplay between the genome and its regulatory factors to effectively control gene expression and silencing. In this review I describe our current state of knowledge with regard to the organization of chromosomes within the nucleus and the positioning of active versus inactive genes. In addition, I discuss studies on the dynamics of chromosomes and specific genetic loci within living cells and its relationship to gene activity and the cell cycle. Furthermore, our current understanding of the distribution and dynamics of RNA polymerase II transcription factors is discussed in relation to chromosomal loci and other nuclear domains

Bridge Over Troubled Skies: Satellite Broadband and the Digital Divide

A few years ago, at the height of the Internet boom, pundits often spoke of Internet time. They meant many things by this reference, but certainly there was a recognition that a key strength of the Internet is the fast communications speeds involved. While the concept of Internet time has faded somewhat with the bloom on the Internet rose, it is still the case that ever-increasing numbers of Americans and others in the world have access to high-speed Internet services. Through this access, they are able to refer quickly to a myriad of resources that have made the Internet an essential part of all of our daily lives

A BPS Interpretation of Shape Invariance

We show that shape invariance appears when a quantum mechanical model is invariant under a centrally extended superalgebra endowed with an additional symmetry generator, which we dub the shift operator. The familiar mathematical and physical results of shape invariance then arise from the BPS structure associated with this shift operator. The shift operator also ensures that there is a one-to-one correspondence between the energy levels of such a model and the energies of the BPS-saturating states. These findings thus provide a more comprehensive algebraic setting for understanding shape invariance.Comment: 15 pages, 2 figures, LaTe

A genetic locus targeted to the nuclear periphery in living cells maintains its transcriptional competence

The peripheral nuclear lamina, which is largely but not entirely associated with inactive chromatin, is considered to be an important determinant of nuclear structure and gene expression. We present here an inducible system to target a genetic locus to the nuclear lamina in living mammalian cells. Using three-dimensional time-lapse microscopy, we determined that targeting of the locus requires passage through mitosis. Once targeted, the locus remains anchored to the nuclear periphery in interphase as well as in daughter cells after passage through a subsequent mitosis. Upon transcriptional induction, components of the gene expression machinery are recruited to the targeted locus, and we visualized nascent transcripts at the nuclear periphery. The kinetics of transcriptional induction at the nuclear lamina is similar to that observed at an internal nuclear region. This new cell system provides a powerful approach to study the dynamics of gene function at the nuclear periphery in living cells