Focusing on contraction

Focusing [1] is a proof-theoretic device to structure proof search in the sequent calculus: it provides a normal form to cut-free proofs in which the application of invertible and non-invertible inference rules is structured in two separate and disjoint phases. It is commonly believed that every \u201creasonable\u201d sequent calculus has a natural focused version. Although stemming from proof-search considerations, focusing has not been thoroughly investigated in actual theorem proving, in particular w.r.t. termination, if not for the folk observations that only negative formulas need to be duplicated (or contracted if seen from the top down) in the focusing phase. We present a contraction-free (and hence terminating) focused proof system for multi-succedent propositional intuitionistic logic, which refines the G4ip calculus of Vorob\u2019ev, Hudelmeier and Dyckhoff. We prove the completeness of the approach semantically and argue that this offers a viable alternative to other more syntactical means

Lens optics as an optical computer for group contractions

It is shown that the one-lens system in para-axial optics can serve as an optical computer for contraction of Wigner's little groups and an analogue computer which transforms analytically computations on a spherical surface to those on a hyperbolic surface. It is shown possible to construct a set of Lorentz transformations which leads to a two-by-two matrix whose expression is the same as those in the para-axial lens optics. It is shown that the lens focal condition corresponds to the contraction of the O(3)-like little group for a massive particle to the E(2)-like little group for a massless particle, and also to the contraction of the O(2,1)-like little group for a space-like particle to the same E(2)-like little group. The lens-focusing transformations presented in this paper allow us to continue analytically the spherical O(3) world to the hyperbolic O(2,1) world, and vice versa.Comment: 14 pages, RevTeX, no figure

Angular Momentum Evolution in Dark Matter Halos

We have analyzed high resolution N-body simulations of dark matter halos, focusing specifically on the evolution of angular momentum. We find that not only is individual particle angular momentum not conserved, but the angular momentum of radial shells also varies over the age of the Universe by up to factors of a few. We find that torques from external structure are the most likely cause for this distribution shift. Since the model of adiabatic contraction that is often applied to model the effects of galaxy evolution on the dark-matter density profile in a halo assumes angular momentum conservation, this variation implies that there is a fundamental limit on the possible accuracy of the adiabatic contraction model in modeling the response of DM halos to the growth of galaxies.Comment: 16 pages, 9 figures, accepted for publication in MNRA

The septin cytoskeleton facilitates membrane retraction during motility and blebbing.

Increasing evidence supports a critical role for the septin cytoskeleton at the plasma membrane during physiological processes including motility, formation of dendritic spines or cilia, and phagocytosis. We sought to determine how septins regulate the plasma membrane, focusing on this cytoskeletal element's role during effective amoeboid motility. Surprisingly, septins play a reactive rather than proactive role, as demonstrated during the response to increasing hydrostatic pressure and subsequent regulatory volume decrease. In these settings, septins were required for rapid cortical contraction, and SEPT6-GFP was recruited into filaments and circular patches during global cortical contraction and also specifically during actin filament depletion. Recruitment of septins was also evident during excessive blebbing initiated by blocking membrane trafficking with a dynamin inhibitor, providing further evidence that septins are recruited to facilitate retraction of membranes during dynamic shape change. This function of septins in assembling on an unstable cortex and retracting aberrantly protruding membranes explains the excessive blebbing and protrusion observed in septin-deficient T cells

Vascular smooth muscle contraction in hypertension

Hypertension is a major risk factor for many common chronic diseases, such as heart failure, myocardial infarction, stroke, vascular dementia and chronic kidney disease. Pathophysiological mechanisms contributing to the development of hypertension include increased vascular resistance, determined in large part by reduced vascular diameter due to increased vascular contraction and arterial remodelling. These processes are regulated by complex interacting systems such as the renin angiotensin aldosterone system (RAAS), sympathetic nervous system, immune activation and oxidative stress, which influence vascular smooth muscle function. Vascular smooth muscle cells are highly plastic and in pathological conditions undergo phenotypic changes from a contractile to a proliferative state. Vascular smooth muscle contraction is triggered by an increase in intracellular free calcium concentration ([Ca2+]i), promoting actin-myosin cross-bridge formation. Growing evidence indicates that contraction is also regulated by calcium-independent mechanisms involving RhoA-Rho kinase (ROCK), protein kinase C (PKC) and mitogen-activated protein kinase (MAPK) signaling, reactive oxygen species and reorganization of the actin cytoskeleton. Activation of immune/inflammatory pathways and noncoding RNAs are also emerging as important regulators of vascular function. Vascular smooth muscle cell [Ca2+]i, not only determines the contractile state but also influences activity of many calcium-dependent transcription factors and proteins thereby impacting the cellular phenotype and function. Perturbations in vascular smooth muscle cell signaling and altered function influence vascular reactivity and tone, important determinants of vascular resistance and blood pressure. Here we discuss mechanisms regulating vascular reactivity and contraction in physiological and pathophysiological conditions and highlight some new advances in the field, focusing specifically on hypertension

Magnetic tension and gravitational collapse

The gravitational collapse of a magnetised medium is investigated by studying qualitatively the convergence of a timelike family of non-geodesic worldlines in the presence of a magnetic field. Focusing on the field's tension we illustrate how the winding of the magnetic forcelines due to the fluid's rotation assists the collapse, while shear-like distortions in the distribution of the field's gradients resist contraction. We also show that the relativistic coupling between magnetism and geometry, together with the tension properties of the field, lead to a magneto-curvature stress that opposes the collapse. This tension stress grows stronger with increasing curvature distortion, which means that it could potentially dominate over the gravitational pull of the matter. If this happens, a converging family of non-geodesic lines can be prevented from focusing without violating the standard energy conditions.Comment: Typos corrected. Published versio

Cross-sectional focusing of red blood cells in a constricted microfluidic channel

Constrictions in blood vessels and microfluidic devices can dramatically change the spatial distribution of passing cells or particles and are commonly used in biomedical cell sorting applications. However, the three-dimensional nature of cell focusing in the channel cross-section remains poorly investigated. Here, we explore the cross-sectional distribution of living and rigid red blood cells passing a constricted microfluidic channel by tracking individual cells in multiple layers across the channel depth and across the channel width. While cells are homogeneously distributed in the channel cross-section pre-contraction, we observe a strong geometry-induced focusing towards the four channel faces post-contraction. The magnitude of this cross-sectional focusing effect increases with increasing Reynolds number for both living and rigid red blood cells. We discuss how this non-uniform cell distribution downstream of the contraction results in an apparent double-peaked velocity profile in particle image velocimetry analysis and show that trapping of red blood cells in the recirculation zones of the abrupt construction depends on cell deformability.Comment: accepted for soft matte