Colloidal transport through optical tweezer arrays

Viscously damped particles driven past an evenly spaced array of potential energy wells or barriers may become kinetically locked in to the array, or else may escape from the array. The transition between locked-in and free-running states has been predicted to depend sensitively on the ratio between the particles' size and the separation between wells. This prediction is confirmed by measurements on monodisperse colloidal spheres driven through arrays of holographic optical traps.Comment: 4 pages, 4 figure

Degenerate flag varieties and the median Genocchi numbers

We study the \bG_a^M degenerations \Fl^a_\la of the type $A$ flag varieties \Fl_\la. We describe these degenerations explicitly as subvarieties in the products of Grassmanians. We construct cell decompositions of \Fl^a_\la and show that for complete flags the number of cells is equal to the normalized median Genocchi numbers $h_n$. This leads to a new combinatorial definition of the numbers $h_n$. We also compute the Poincar\' e polynomials of the complete degenerate flag varieties via a natural statistics on the set of Dellac's configurations, similar to the length statistics on the set of permutations. We thus obtain a natural $q$-version of the normalized median Genocchi numbers.Comment: 18 page

A Tale of Two Tilings

What do you get when you cross a crystal with a quasicrystal? The surprising answer stretches from Fibonacci to Kepler, who nearly 400 years ago showed how the ancient tiles of Archimedes form periodic patterns.Comment: 3 pages, 1 figur

Transitive and Gallai colorings

A Gallai coloring of the complete graph is an edge-coloring with no rainbow triangle. This concept first appeared in the study of comparability graphs and anti-Ramsey theory. We introduce a transitive analogue for acyclic directed graphs, and generalize both notions to Coxeter systems, matroids and commutative algebras. It is shown that for any finite matroid (or oriented matroid), the maximal number of colors is equal to the matroid rank. This generalizes a result of Erd\H{o}s-Simonovits-S\'os for complete graphs. The number of Gallai (or transitive) colorings of the matroid that use at most $k$ colors is a polynomial in $k$. Also, for any acyclic oriented matroid, represented over the real numbers, the number of transitive colorings using at most 2 colors is equal to the number of chambers in the dual hyperplane arrangement. We count Gallai and transitive colorings of the root system of type A using the maximal number of colors, and show that, when equipped with a natural descent set map, the resulting quasisymmetric function is symmetric and Schur-positive.Comment: 31 pages, 5 figure

Hydrodynamic Pair Attractions Between Driven Colloidal Particles

Colloidal spheres driven through water along a circular path by an optical ring trap display unexpected dynamical correlations. We use Stokesian Dynamics simulations and a simple analytical model to demonstrate that the path's curvature breaks the symmetry of the two-body hydrodynamic interaction, resulting in particle pairing. The influence of this effective nonequilibrium attraction diminishes as either the temperature or the stiffness of the radial confinement increases. We find a well defined set of dynamically paired states whose stability relies on hydrodynamic coupling in curving trajectories.Comment: 5 pages, 4 figure

Restoration of energy homeostasis by SIRT6 extends healthy lifespan

Aging leads to a gradual decline in physical activity and disrupted energy homeostasis. The NAD+-dependent SIRT6 deacylase regulates aging and metabolism through mechanisms that largely remain unknown. Here, we show that SIRT6 overexpression leads to a reduction in frailty and lifespan extension in both male and female B6 mice. A combination of physiological assays, in vivo multi-omics analyses and 13C lactate tracing identified an age-dependent decline in glucose homeostasis and hepatic glucose output in wild type mice. In contrast, aged SIRT6-transgenic mice preserve hepatic glucose output and glucose homeostasis through an improvement in the utilization of two major gluconeogenic precursors, lactate and glycerol. To mediate these changes, mechanistically, SIRT6 increases hepatic gluconeogenic gene expression, de novo NAD+ synthesis, and systemically enhances glycerol release from adipose tissue. These findings show that SIRT6 optimizes energy homeostasis in old age to delay frailty and preserve healthy aging

SIRT6 Promotes Hepatic Beta-Oxidation via Activation of PPARα

The pro-longevity enzyme SIRT6 regulates various metabolic pathways. Gene expression analyses in SIRT6 heterozygotic mice identify significant decreases in PPARα signaling, known to regulate multiple metabolic pathways. SIRT6 binds PPARα and its response element within promoter regions and activates gene transcription. Sirt6+/− results in significantly reduced PPARα-induced β-oxidation and its metabolites and reduced alanine and lactate levels, while inducing pyruvate oxidation. Reciprocally, starved SIRT6 transgenic mice show increased pyruvate, acetylcarnitine, and glycerol levels and significantly induce β-oxidation genes in a PPARα-dependent manner. Furthermore, SIRT6 mediates PPARα inhibition of SREBP-dependent cholesterol and triglyceride synthesis. Mechanistically, SIRT6 binds PPARα coactivator NCOA2 and decreases liver NCOA2 K780 acetylation, which stimulates its activation of PPARα in a SIRT6-dependent manner. These coordinated SIRT6 activities lead to regulation of whole-body respiratory exchange ratio and liver fat content, revealing the interactions whereby SIRT6 synchronizes various metabolic pathways, and suggest a mechanism by which SIRT6 maintains healthy liver

The absolute order of a permutation representation of a Coxeter group

A permutation representation of a Coxeter group W naturally defines an absolute order. This family of partial orders (which includes the absolute order on W) is introduced and studied in this paper. Conditions under which the associated rank generating polynomial divides the rank generating polynomial of the absolute order on W are investigated when W is finite. Several examples, including a symmetric group action on perfect matchings, are discussed. As an application, a well-behaved absolute order on the alternating subgroup of W is defined. © 2013 Springer Science+Business Media New York