Interplay of interactions and disorder at the superfluid-insulator transition: A dirty two-dimensional quantum critical point

We study the stability of the Wilson-Fisher fixed point of the quantum O(2N) vector model to quenched disorder in the large-N limit. While a random mass is strongly relevant at the Gaussian fixed point, its effect is screened by the strong interactions of the Wilson-Fisher fixed point. This enables a perturbative renormalization group study of the interplay of disorder and interactions about this fixed point. We show that, in contrast to the spiralling flows obtained in earlier double-ε expansions, the theory flows directly to a quantum critical point characterized by finite disorder and interactions. The critical exponents we obtain for this transition are in remarkable agreement with numerical studies of the superfluid-Mott glass transition. We additionally discuss the stability of this fixed point to scalar and vector potential disorder and use proposed boson-fermion dualities to make conjectures regarding the effects of weak disorder on dual Abelian Higgs and Chern-Simons-Dirac fermion theories when N = 1

Unsupervised discovery of temporal sequences in high-dimensional datasets, with applications to neuroscience.

Identifying low-dimensional features that describe large-scale neural recordings is a major challenge in neuroscience. Repeated temporal patterns (sequences) are thought to be a salient feature of neural dynamics, but are not succinctly captured by traditional dimensionality reduction techniques. Here, we describe a software toolbox-called seqNMF-with new methods for extracting informative, non-redundant, sequences from high-dimensional neural data, testing the significance of these extracted patterns, and assessing the prevalence of sequential structure in data. We test these methods on simulated data under multiple noise conditions, and on several real neural and behavioral datas. In hippocampal data, seqNMF identifies neural sequences that match those calculated manually by reference to behavioral events. In songbird data, seqNMF discovers neural sequences in untutored birds that lack stereotyped songs. Thus, by identifying temporal structure directly from neural data, seqNMF enables dissection of complex neural circuits without relying on temporal references from stimuli or behavioral outputs

Anisotropic thermodynamic and transport properties of single crystalline CaKFe4_{4}As4_{4}

Single crystalline, single phase CaKFe$_{4}$As$_{4}$ has been grown out of a high temperature, quaternary melt. Temperature dependent measurements of x-ray diffraction, anisotropic electrical resistivity, elastoresistivity, thermoelectric power, Hall effect, magnetization and specific heat, combined with field dependent measurements of electrical resistivity and field and pressure dependent measurements of magnetization indicate that CaKFe$_{4}$As$_{4}$ is an ordered, stoichiometric, Fe-based superconductor with a superconducting critical temperature, $T_c$ = 35.0 $\pm$ 0.2 K. Other than superconductivity, there is no indication of any other phase transition for 1.8 K $\leq T \leq$ 300 K. All of these thermodynamic and transport data reveal striking similarities to that found for optimally- or slightly over-doped (Ba$_{1-x}$K$_x$)Fe$_2$As$_2$, suggesting that stoichiometric CaKFe$_4$As$_4$ is intrinsically close to what is referred to as "optimal-doped" on a generalized, Fe-based superconductor, phase diagram. The anisotropic superconducting upper critical field, $H_{c\text{2}}(T)$, of CaKFe$_{4}$As$_{4}$ was determined up to 630 kOe. The anisotropy parameter $\gamma(T)=H_{c\text{2}}^{\perp}/H_{c\text{2}}^{\|}$, for $H$ applied perpendicular and parallel to the c-axis, decreases from $\simeq 2.5$ at $T_c$ to $\simeq 1.5$ at 25 K which can be explained by interplay of paramagnetic pairbreaking and orbital effects. The slopes of $dH_{c\text{2}}^{\|}/dT\simeq-44$ kOe/K and $dH_{c\text{2}}^{\perp}/dT \simeq-109$ kOe/K at $T_c$ yield an electron mass anisotropy of $m_{\perp}/m_{\|}\simeq 1/6$ and short Ginzburg-Landau coherence lengths $\xi_{\|}(0)\simeq 5.8 \text{\AA}$ and $\xi_{\perp}(0)\simeq 14.3 \text{\AA}$. The value of $H_{c\text{2}}^{\perp}(0)$ can be extrapolated to $\simeq 920$ kOe, well above the BCS paramagnetic limit.Comment: 13 pages, 15 figures, part of arXiv:1606.02241 is include

Quark Coulomb Interactions and the Mass Difference of Mirror Nuclei

We study the Okamoto-Nolen-Schiffer (ONS) anomaly in the binding energy of mirror nuclei at high density by adding a single neutron or proton to a quark gluon plasma. In this high-density limit we find an anomaly equal to two-thirds of the Coulomb exchange energy of a proton. This effect is dominated by quark electromagnetic interactions---rather than by the up-down quark mass difference. At normal density we calculate the Coulomb energy of neutron matter using a string-flip quark model. We find a nonzero Coulomb energy because of the neutron's charged constituents. This effect could make a significant contribution to the ONS anomaly.Comment: 4 pages, 2 figs. sub. to Phys. Rev. Let

Lift-off dynamics in a simple jumping robot

We study vertical jumping in a simple robot comprising an actuated mass-spring arrangement. The actuator frequency and phase are systematically varied to find optimal performance. Optimal jumps occur above and below (but not at) the robot's resonant frequency $f_0$. Two distinct jumping modes emerge: a simple jump which is optimal above $f_0$ is achievable with a squat maneuver, and a peculiar stutter jump which is optimal below $f_0$ is generated with a counter-movement. A simple dynamical model reveals how optimal lift-off results from non-resonant transient dynamics.Comment: 4 pages, 4 figures, Physical Review Letters, in press (2012

TRI-PLANE DIAGRAMS FOR SIMPLE SURFACES IN \u3ci\u3eS\u3c/i\u3e\u3csup\u3e4\u3c/sup\u3e

Meier and Zupan proved that an orientable surface K in S4 admits a tri-plane diagram with zero crossings if and only if K is unknotted, so that the crossing number of K is zero. We determine the minimal crossing numbers of nonorientable unknotted surfaces in S4, proving that c(Pn,m) = max{1, |n−m|}, where Pn,m denotes the connected sum of n unknotted projective planes with normal Euler number +2 and m unknotted projective planes with normal Euler number −2. In addition, we convert Yoshikawa’s table of knotted surface ch-diagrams to tri-plane diagrams, finding the minimal bridge number for each surface in the table and providing upper bounds for the crossing numbers

PTCHD1 Binds Cholesterol but Not Sonic Hedgehog, Suggesting a Distinct Cellular Function

Deleterious mutations in the X-linked Patched domain-containing 1 (PTCHD1) gene may account for up to 1% of autism cases. Despite this, the PTCHD1 protein remains poorly understood. Structural similarities to Patched family proteins point to a role in sterol transport, but this hypothesis has not been verified experimentally. Additionally, PTCHD1 has been suggested to be involved in Hedgehog signalling, but thus far, the experimental results have been conflicting. To enable a variety of biochemical and structural experiments, we developed a method for expressing PTCHD1 in Spodoptera frugiperda cells, solubilising it in glycol-diosgenin, and purifying it to homogeneity. In vitro and in silico experiments show that PTCHD1 function is not interchangeable with Patched 1 (PTCH1) in canonical Hedgehog signalling, since it does not repress Smoothened in Ptch1−/− mouse embryonic fibroblasts and does not bind Sonic Hedgehog. However, we found that PTCHD1 binds cholesterol similarly to PTCH1. Furthermore, we identified 13 PTCHD1-specific protein interactors through co-immunoprecipitation and demonstrated a link to cell stress responses and RNA stress granule formation. Thus, our results support the notion that despite structural similarities to other Patched family proteins, PTCHD1 may have a distinct cellular function