Knot Theory: from Fox 3-colorings of links to Yang-Baxter homology and Khovanov homology

This paper is an extended account of my "Introductory Plenary talk at Knots in Hellas 2016" conference We start from the short introduction to Knot Theory from the historical perspective, starting from Heraclas text (the first century AD), mentioning R.Llull (1232-1315), A.Kircher (1602-1680), Leibniz idea of Geometria Situs (1679), and J.B.Listing (student of Gauss) work of 1847. We spend some space on Ralph H. Fox (1913-1973) elementary introduction to diagram colorings (1956). In the second section we describe how Fox work was generalized to distributive colorings (racks and quandles) and eventually in the work of Jones and Turaev to link invariants via Yang-Baxter operators, here the importance of statistical mechanics to topology will be mentioned. Finally we describe recent developments which started with Mikhail Khovanov work on categorification of the Jones polynomial. By analogy to Khovanov homology we build homology of distributive structures (including homology of Fox colorings) and generalize it to homology of Yang-Baxter operators. We speculate, with supporting evidence, on co-cycle invariants of knots coming from Yang-Baxter homology. Here the work of Fenn-Rourke-Sanderson (geometric realization of pre-cubic sets of link diagrams) and Carter-Kamada-Saito (co-cycle invariants of links) will be discussed and expanded. Dedicated to Lou Kauffman for his 70th birthday.Comment: 35 pages, 31 figures, for Knots in Hellas II Proceedings, Springer, part of the series Proceedings in Mathematics & Statistics (PROMS

Unsteady effects during resistance tests on a ship model in a towing tank

It is known that there are oscillations in the wave resistance during the constantvelocity phase of a towing-tank resistance test on a ship model. In this work, the unsteady thin-ship resistance theory has been applied to this case. The results have been compared with experiment data obtained using a towing carriage the velocity history of which can be programmed. It is demonstrated here that generally excellent correlation exists between the theory and the experiments. In particular, one can predict the influence of Froude number, rate of acceleration, and type of smoothing of the acceleration on the characteristics of the oscillations. These characteristics include the amplitude, rate of decay, frequency, and phasing of the oscillations in the curve of wave resistance versus time

FGF signalling through RAS/MAPK and PI3K pathways regulates cell movement and gene expression in the chicken primitive streak without affecting E-cadherin expression

<p>Abstract</p> <p>Background</p> <p>FGF signalling regulates numerous aspects of early embryo development. During gastrulation in amniotes, epiblast cells undergo an epithelial to mesenchymal transition (EMT) in the primitive streak to form the mesoderm and endoderm. In mice lacking FGFR1, epiblast cells in the primitive streak fail to downregulate E-cadherin and undergo EMT, and cell migration is inhibited. This study investigated how FGF signalling regulates cell movement and gene expression in the primitive streak of chicken embryos.</p> <p>Results</p> <p>We find that pharmacological inhibition of FGFR activity blocks migration of cells through the primitive streak of chicken embryos without apparent alterations in the level or intracellular localization of E-cadherin. E-cadherin protein is localized to the periphery of epiblast, primitive streak and some mesodermal cells. FGFR inhibition leads to downregulation of a large number of regulatory genes in the preingression epiblast adjacent to the primitive streak, the primitive streak and the newly formed mesoderm. This includes members of the FGF, NOTCH, EPH, PDGF, and canonical and non-canonical WNT pathways, negative modulators of these pathways, and a large number of transcriptional regulatory genes. <it>SNAI2 </it>expression in the primitive streak and mesoderm is not altered by FGFR inhibition, but is downregulated only in the preingression epiblast region with no significant effect on E-cadherin. Furthermore, over expression of SNAIL has no discernable effect on E-cadherin protein levels or localization in epiblast, primitive streak or mesodermal cells. FGFR activity modulates distinct downstream pathways including RAS/MAPK and PI3K/AKT. Pharmacological inhibition of MEK or AKT indicate that these downstream effectors control discrete and overlapping groups of genes during gastrulation. FGFR activity regulates components of several pathways known to be required for cell migration through the streak or in the mesoderm, including RHOA, the non-canonical WNT pathway, PDGF signalling and the cell adhesion protein N-cadherin.</p> <p>Conclusions</p> <p>In chicken embryos, FGF signalling regulates cell movement through the primitive streak by mechanisms that appear to be independent of changes in E-cadherin expression or protein localization. The positive and negative effects on large groups of genes by pharmacological inhibition of FGF signalling, including major signalling pathways and transcription factor families, indicates that the FGF pathway is a focal point of regulation during gastrulation in chicken.</p

Connecting radio emission to AGN wind properties with Broad Absorption Line Quasars

Broad Absorption Line Quasars (BALQSOs) show strong signatures of powerful outflows, with the potential to alter the cosmic history of their host galaxies. These signatures are only seen in ∼10% of optically selected quasars, although the fraction significantly increases in IR and radio selected samples. A proven physical explanation for this observed fraction has yet to be found, along with a determination of why this fraction increases at radio wavelengths. We present the largest sample of radio matched BALQSOs using the LOFAR Two-metre Sky Survey Data Release 2 and employ it to investigate radio properties of BALQSOs. Within the DR2 footprint, there are 3537 BALQSOs from Sloan Digital Sky Survey DR12 with continuum signal to noise ≥5. We find radio-detections for 1108 BALQSOs, with an important sub-population of 120 LoBALs, an unprecedented sample size for radio matched BALQSOs given the sky coverage to date. BALQSOs are a radio-quiet population that show an increase of × 1.50 radio-detection fraction compared to non-BALQSOs. LoBALs show an increase of × 2.22 that of non-BALQSO quasars. We show that this detection fraction correlates with wind-strength, reddening and C IV emission properties of BALQSOs and that these features may be connected, although no single property can fully explain the enhanced radio detection fraction. We create composite spectra for sub-classes of BALQSOs based on wind strength and colour, finding differences in the absorption profiles of radio-detected and radio-undetected sources, particularly for LoBALs. Overall, we favour a wind-ISM interaction explanation for the increased radio-detection fraction of BALQSOs

Links between traumatic brain injury and ballistic pressure waves originating in the thoracic cavity and extremities

Identifying patients at risk of traumatic brain injury (TBI) is important because research suggests prophylactic treatments to reduce risk of long-term sequelae. Blast pressure waves can cause TBI without penetrating wounds or blunt force trauma. Similarly, bullet impacts distant from the brain can produce pressure waves sufficient to cause mild to moderate TBI. The fluid percussion model of TBI shows that pressure impulses of 15-30 psi cause mild to moderate TBI in laboratory animals. In pigs and dogs, bullet impacts to the thigh produce pressure waves in the brain of 18-45 psi and measurable injury to neurons and neuroglia. Analyses of research in goats and epidemiological data from shooting events involving humans show high correlations (r > 0.9) between rapid incapacitation and pressure wave magnitude in the thoracic cavity. A case study has documented epilepsy resulting from a pressure wave without the bullet directly hitting the brain. Taken together, these results support the hypothesis that bullet impacts distant from the brain produce pressure waves that travel to the brain and can retain sufficient magnitude to induce brain injury. The link to long-term sequelae could be investigated via epidemiological studies of patients who were gunshot in the chest to determine whether they experience elevated rates of epilepsy and other neurological sequelae

Finding and Resolving Security Misusability with Misusability Cases

Although widely used for both security and usability concerns, scenarios used in security design may not necessarily inform the design of usability, and vice- versa. One way of using scenarios to bridge security and usability involves explicitly describing how design deci- sions can lead to users inadvertently exploiting vulnera- bilities to carry out their production tasks. This paper describes how misusability cases, scenarios that describe how design decisions may lead to usability problems sub- sequently leading to system misuse, address this problem. We describe the related work upon which misusability cases are based before presenting the approach, and illus- trating its application using a case study example. Finally, we describe some findings from this approach that further inform the design of usable and secure systems

Inside-Out Evacuation of Transitional Protoplanetary Disks by the Magneto-Rotational Instability

How do T Tauri disks accrete? The magneto-rotational instability (MRI) supplies one means, but protoplanetary disk gas is typically too poorly ionized to be magnetically active. Here we show that the MRI can, in fact, explain observed accretion rates for the sub-class of T Tauri disks known as transitional systems. Transitional disks are swept clean of dust inside rim radii of ~10 AU. Stellar coronal X-rays ionize material in the disk rim, activating the MRI there. Gas flows from the rim to the star, at a rate limited by the depth to which X-rays ionize the rim wall. The wider the rim, the larger the surface area that the rim wall exposes to X-rays, and the greater the accretion rate. Interior to the rim, the MRI continues to transport gas; the MRI is sustained even at the disk midplane by super-keV X-rays that Compton scatter down from the disk surface. Accretion is therefore steady inside the rim. Blown out by radiation pressure, dust largely fails to accrete with gas. Contrary to what is usually assumed, ambipolar diffusion, not Ohmic dissipation, limits how much gas is MRI-active. We infer values for the transport parameter alpha on the order of 0.01 for GM Aur, TW Hyd, and DM Tau. Because the MRI can only afflict a finite radial column of gas at the rim, disk properties inside the rim are insensitive to those outside. Thus our picture provides one robust setting for planet-disk interaction: a protoplanet interior to the rim will interact with gas whose density, temperature, and transport properties are definite and decoupled from uncertain initial conditions. Our study also supplies half the answer to how disks dissipate: the inner disk drains from the inside out by the MRI, while the outer disk photoevaporates by stellar ultraviolet radiation.Comment: Accepted to Nature Physics June 7, 2007. The manuscript for publication is embargoed per Nature policy. This arxiv.org version contains more technical details and discussion, and is distributed with permission from the editors. 10 pages, 4 figure

HOMFLY and superpolynomials for figure eight knot in all symmetric and antisymmetric representations

Explicit answer is given for the HOMFLY polynomial of the figure eight knot $4_1$ in arbitrary symmetric representation R=[p]. It generalizes the old answers for p=1 and 2 and the recently derived results for p=3,4, which are fully consistent with the Ooguri-Vafa conjecture. The answer can be considered as a quantization of the \sigma_R = \sigma_{[1]}^{|R|} identity for the "special" polynomials (they define the leading asymptotics of HOMFLY at q=1), and arises in a form, convenient for comparison with the representation of the Jones polynomials as sums of dilogarithm ratios. In particular, we construct a difference equation ("non-commutative A-polynomial") in the representation variable p. Simple symmetry transformation provides also a formula for arbitrary antisymmetric (fundamental) representation R=[1^p], which also passes some obvious checks. Also straightforward is a deformation from HOMFLY to superpolynomials. Further generalizations seem possible to arbitrary Young diagrams R, but these expressions are harder to test because of the lack of alternative results, even partial.Comment: 14 page

Sensory Electrical Stimulation Improves Foot Placement during Targeted Stepping Post-Stroke

Proper foot placement is vital for maintaining balance during walking, requiring the integration of multiple sensory signals with motor commands. Disruption of brain structures post-stroke likely alters the processing of sensory information by motor centers, interfering with precision control of foot placement and walking function for stroke survivors. In this study, we examined whether somatosensory stimulation, which improves functional movements of the paretic hand, could be used to improve foot placement of the paretic limb. Foot placement was evaluated before, during, and after application of somatosensory electrical stimulation to the paretic foot during a targeted stepping task. Starting from standing, twelve chronic stroke participants initiated movement with the non-paretic limb and stepped to one of five target locations projected onto the floor with distances normalized to the paretic stride length. Targeting error and lower extremity kinematics were used to assess changes in foot placement and limb control due to somatosensory stimulation. Significant reductions in placement error in the medial–lateral direction (p = 0.008) were observed during the stimulation and post-stimulation blocks. Seven participants, presenting with a hip circumduction walking pattern, had reductions (p = 0.008) in the magnitude and duration of hip abduction during swing with somatosensory stimulation. Reductions in circumduction correlated with both functional and clinical measures, with larger improvements observed in participants with greater impairment. The results of this study suggest that somatosensory stimulation of the paretic foot applied during movement can improve the precision control of foot placement

Hands-On Parameter Search for Neural Simulations by a MIDI-Controller

Computational neuroscientists frequently encounter the challenge of parameter fitting – exploring a usually high dimensional variable space to find a parameter set that reproduces an experimental data set. One common approach is using automated search algorithms such as gradient descent or genetic algorithms. However, these approaches suffer several shortcomings related to their lack of understanding the underlying question, such as defining a suitable error function or getting stuck in local minima. Another widespread approach is manual parameter fitting using a keyboard or a mouse, evaluating different parameter sets following the users intuition. However, this process is often cumbersome and time-intensive. Here, we present a new method for manual parameter fitting. A MIDI controller provides input to the simulation software, where model parameters are then tuned according to the knob and slider positions on the device. The model is immediately updated on every parameter change, continuously plotting the latest results. Given reasonably short simulation times of less than one second, we find this method to be highly efficient in quickly determining good parameter sets. Our approach bears a close resemblance to tuning the sound of an analog synthesizer, giving the user a very good intuition of the problem at hand, such as immediate feedback if and how results are affected by specific parameter changes. In addition to be used in research, our approach should be an ideal teaching tool, allowing students to interactively explore complex models such as Hodgkin-Huxley or dynamical systems