Condensate fraction in a 2D Bose gas measured across the Mott-insulator transition

We realize a single-band 2D Bose-Hubbard system with Rb atoms in an optical lattice and measure the condensate fraction as a function of lattice depth, crossing from the superfluid to the Mott-insulating phase. We quantitatively identify the location of the superfluid to normal transition by observing when the condensed fraction vanishes. Our measurement agrees with recent quantum Monte Carlo calculations for a finite-sized 2D system to within experimental uncertainty.     

An elementary proof of the restricted invertibility theorem

We give an elementary proof of a generalization of Bourgain and Tzafriri’s Restricted Invertibility Theorem, which says roughly that any matrix with columns of unit length and bounded operator norm has a large coordinate subspace on which it is well-invertible. Our proof gives the tightest known form of this result, is constructive, and provides a deterministic polynomial time algorithm for finding the desired subspace.     

Realistic time-reversal invariant topological insulators with neutral atoms

We lay out an experiment to realize time-reversal invariant topological insulators in alkali atomic gases. We introduce an original method to synthesize a gauge field in the near field of an atom chip, which effectively mimics the effects of spin-orbit coupling and produces quantum spin-Hall states. We also propose a feasible scheme to engineer sharp boundaries where the hallmark edge states are localized. Our multiband system has a large parameter space exhibiting a variety of quantum phase transitions between topological and normal insulating phases. Because of their remarkable versatility, cold-atom systems are ideally suited to realize topological states of matter and drive the development of topological quantum computing.     

Korringa-like nuclear spin–lattice relaxation in a 2DES at

Via a resistively detected NMR technique, the nuclear spin–lattice relaxation time T₁ of ⁷¹Ga has been measured in a GaAs/AlGaAs heterostructure containing two weakly coupled 2D electron systems (2DES) at low temperatures, each at Landau level filling . Incomplete electronic spin polarization, which has been reported previously for low density 2DESs at , should facilitate hyperfine-coupled nuclear spin relaxation owing to the presence of both electron spin states at the Fermi level. Composite fermion theory suggests a Korringa-law temperature dependence: T₁T=constant is expected for temperatures . Our measurements show that for temperatures in the range , T₁ rises less rapidly with falling temperature than this law predicts. This may suggest the existence of alternate nuclear spin relaxation mechanisms in this system. Also, our data allows for an estimate of the composite fermion mass.     

Smoothed analysis of condition numbers and complexity implications for linear programming

We perform a smoothed analysis of Renegar’s condition number for linear programming by analyzing the distribution of the distance to ill-posedness of a linear program subject to a slight Gaussian perturbation. In particular, we show that for every n-by-d matrix Ā, n-vector [`(\varvec b)]{\bar{\varvec b}}, and d-vector [`(\varvec c)]{\bar{\varvec c}} satisfying ||[`(A)], [`(\varvec b)], [`(\varvec c)]||_F ￡ 1{{||\bar{\bf A}, \bar{\varvec b}, \bar{\varvec c}||_F \leq 1}} and every σ ≤ 1,

Fast multivoxel two-dimensional spectroscopic imaging at 3 T

The utility of multivoxel two-dimensional chemical shift imaging in the clinical environment will ultimately be determined by the imaging time and the metabolite peaks that can be detected. Different k-space sampling schemes can be characterized by their minimum required imaging time. The use of spiral-based readout gradients effectively reduces the minimum scan time required due to simultaneous data acquisition in three k-space dimensions (k(x), k(y) and k(f(2))). A 3-T spiral-based multivoxel two-dimensional spectroscopic imaging sequence using the PRESS excitation scheme was implemented. Good performance was demonstrated by acquiring preliminary in vivo data for applications, including brain glutamate imaging, metabolite T(2) quantification and high-spatial-resolution prostate spectroscopic imaging. All protocols were designed to acquire data within a 17-min scan time at a field strength of 3 T.     

The feasibility of assessing branched-chain amino acid metabolism in cellular models of prostate cancer with hyperpolarized [1-C]-ketoisocaproate

Recent advancements in the field of hyperpolarized ¹³C magnetic resonance spectroscopy (MRS) have yielded powerful techniques capable of real-time analysis of metabolic pathways. These non-invasive methods have increasingly shown application in impacting disease diagnosis and have further been employed in mechanistic studies of disease onset and progression. Our goals were to investigate branched-chain aminotransferase (BCAT) activity in prostate cancer with a novel molecular probe, hyperpolarized [1-¹³C]-2-ketoisocaproate ([1-¹³C]-KIC), and explore the potential of branched-chain amino acid (BCAA) metabolism to serve as a biomarker. Using traditional spectrophotometric assays, BCAT enzymatic activities were determined in vitro for various sources of prostate cancer (human, transgenic adenocarcinoma of the mouse prostate (TRAMP) mouse and human cell lines). These preliminary studies indicated that low levels of BCAT activity were present in all models of prostate cancer but enzymatic levels are altered significantly in prostate cancer relative to healthy tissue. The MR spectroscopic studies were conducted with two cellular models (PC-3 and DU-145) that exhibited levels of BCAA metabolism comparable to the human disease state. Hyperpolarized [1-¹³C]-KIC was administered to prostate cancer cell lines, and the conversion of [1-¹³C]-KIC to the metabolic product, [1-¹³C]-leucine ([1-¹³C]-Leu), could be monitored via hyperpolarized ¹³C MRS.     

Location coverage models with demand originating from nodes and paths: Application to cellular network design

Location covering problems, though well studied in the literature, typically consider only nodal (i.e. point) demand coverage. In contrast, we assume that demand occurs from both nodes and paths. We develop two separate models – one that handles the situation explicitly and one which handles it implicitly. The explicit model is formulated as a Quadratic Maximal Covering Location Problem – a greedy heuristic supported by simulated annealing (SA) that locates facilities in a paired fashion at each stage is developed for its solution. The implicit model focuses on systems with network structure – a heuristic algorithm based on geometrical concepts is developed. A set of computational experiments analyzes the performance of the algorithms, for both models. We show, through a case study for locating cellular base stations in Erie County, New York State, USA, how the model can be used for capturing demand from both stationary cell phone users as well as cell phone users who are in moving vehicles.