Orthogonal Type Research Articles

The Noether-Lefschetz conjecture and generalizations

We prove the Noether-Lefschetz conjecture on the moduli space of quasi-polarized K3 surfaces. This is deduced as a particular case of a general theorem that states that low degree cohomology classes of arithmetic manifolds of orthogonal type are dual to the classes of special cycles, i.e. sub-arithmetic manifolds of the same type. For compact manifolds this was proved in [3], here we extend the results of [3] to non-compact manifolds. This allows us to apply our results to the moduli spaces of quasi-polarized K3 surfaces.

Quadratic descent of totally decomposable orthogonal involutions in characteristic two

We investigate the quadratic descent of totally decomposable algebras with involution of orthogonal type in characteristic two. Both separable and inseparable extensions are included.

Guide RNAs: A Glimpse at the Sequences that Drive CRISPR-Cas Systems.

CRISPR-Cas systems provide adaptive immunity in bacteria and archaea. Although there are two main classes of CRISPR-Cas systems defined by gene content, interfering RNA biogenesis, and effector proteins, Type II systems have recently been exploited on a broad scale to develop next-generation genetic engineering and genome-editing tools. Conveniently, Type II systems are streamlined and rely on a single protein, Cas9, and a guide RNA molecule, comprised of a CRISPR RNA (crRNA) and trans-acting CRISPR RNA (tracrRNA), to achieve effective and programmable nucleic acid targeting and cleavage. Currently, most commercially available Cas9-based genome-editing tools use the CRISPR-Cas system from Streptococcus pyogenes (SpyCas9), although many orthogonal Type II systems are available for diverse and multiplexable genome engineering applications. Here, we discuss the biological significance of Type II CRISPR-Cas elements, including the tracrRNA, crRNA, Cas9, and protospacer-adjacent motif (PAM), and look at the native function of these elements to understand how they can be engineered, enhanced, and optimized for genome editing applications. Additionally, we discuss the basis for orthogonal Cas9 and guide RNA systems that would allow researchers to concurrently use multiple Cas9-based systems for different purposes. Understanding the native function of endogenous Type II CRISPR-Cas systems can lead to new Cas9 tool development to expand the genetic manipulation toolbox.

Quorum Sensing Communication Modules for Microbial Consortia.

The power of a single engineered organism is limited by its capacity for genetic modification. To circumvent the constraints of any singular microbe, a new frontier in synthetic biology is emerging: synthetic ecology, or the engineering of microbial consortia. Here we develop communication systems for such consortia in an effort to allow for complex social behavior across different members of a community. We posit that such communities will outpace monocultures in their ability to perform complicated tasks if communication among and between members of the community is well regulated. Quorum sensing was identified as the most promising candidate for precise control of engineered microbial ecosystems, due to its large diversity and established utility in synthetic biology. Through promoter and protein modification, we engineered two quorum sensing systems (rpa and tra) to add to the extensively used lux and las systems. By testing the cross-talk between all systems, we thoroughly characterized many new inducible systems for versatile control of engineered communities. Furthermore, we've identified several system pairs that exhibit useful types of orthogonality. Most notably, the tra and rpa systems were shown to have neither signal crosstalk nor promoter crosstalk for each other, making them completely orthogonal in operation. Overall, by characterizing the interactions between all four systems and their components, these circuits should lend themselves to higher-level genetic circuitry for use in microbial consortia.

On the Oort conjecture for Shimura varieties of unitary and orthogonal types

In this paper we study the Oort conjecture concerning the non-existence of Shimura subvarieties contained generically in the Torelli locus in the Siegel modular variety${\mathcal{A}}_{g}$. Using the poly-stability of Higgs bundles on curves and the slope inequality of Xiao on fibered surfaces, we show that a Shimura curve$C$is not contained generically in the Torelli locus if its canonical Higgs bundle contains a unitary Higgs subbundle of rank at least$(4g+2)/5$. From this we prove that a Shimura subvariety of$\mathbf{SU}(n,1)$type is not contained generically in the Torelli locus when a numerical inequality holds, which involves the genus$g$, the dimension$n+1$, the degree$2d$of CM field of the Hermitian space, and the type of the symplectic representation defining the Shimura subdatum. A similar result holds for Shimura subvarieties of$\mathbf{SO}(n,2)$type, defined by spin groups associated to quadratic spaces over a totally real number field of degree at least$6$subject to some natural constraints of signatures.

On totally decomposable algebras with involution in characteristic two

A necessary and sufficient condition for a central simple algebra with involution over a field of characteristic two to be decomposable as a tensor product of quaternion algebras with involution, in terms of its Frobenius subalgebras, is given. It is also proved that a bilinear Pfister form, recently introduced by A. Dolphin, can classify totally decomposable central simple algebras of orthogonal type.

Line polar Grassmann codes of orthogonal type

Polar Grassmann codes of orthogonal type have been introduced in [1]. They are punctured versions of the Grassmann code arising from the projective system defined by the Plücker embedding of a polar Grassmannian of orthogonal type. In the present paper we fully determine the minimum distance of line polar Grassmann codes of orthogonal type for q odd.

Study of different cross-shaped microchannels affecting thermal-bubble-actuated microparticle manipulation

This paper presents a thermal-bubble-actuated microfluidic chip with cross-shaped microchannels for evaluating the effect of different microchannel designs on microparticle manipulation. Four cross-shaped microchannel designs, with orthogonal, misaligned, skewed, and antiskewed types, were proposed in this study. The thermal bubble micropump, which is based on a resistive bulk microheater, was used to drive fluid transportation, and it can be realized using a simple microfabrication process with a silicon-on-isolator wafer. Using commercial COMSOL software, the flow profiles of microfluidics in various cross-shaped microchannels were simulated qualitatively under different pumping pressures. Microbeads, with a diameter of 20 μm, manipulated in four cross-shaped microchannels, were also implemented in this experiment. The results showed that a skewed microchannel design has a higher sorting rate compared with orthogonal, misaligned, and antiskewed microchannels because its flow velocity in the main microchannel is significantly reduced by pumping pressure. Typically, the successful sorting rate for this type of skewed microchannel can reach 30% at a pumping frequency of 100 Hz.

The perilous leap between exploration and exploitation

Research summary: R&D‐based exploration and exploitation are necessary in order for firms to have sustainable competitive advantage. Yet, transitioning between these orthogonal types of R&D is considered profound organizational change. Building on recent research showing that compact, significant changes in R&D expenditure is an antecedent to the transition between explorative and exploitative R&D, I show that this leap between exploration and exploitation is quite hazardous. The magnitude of changes in R&D expenditure, whether increases or decreases, is positively associated with organizational failure. Firms maintaining higher levels of absorptive capacity are more capable of surviving the leap from R&D‐based exploitation to exploration, and firms that do not use reductions in R&D expenditure to manipulate short‐term earnings performance are more likely to survive the leap from exploration to exploitation.Managerial summary: In order to survive and thrive, innovative companies must be able to exploit their existing competencies, and to explore for new ones once those current competencies decline in value. However, transiting from one form of innovation to the other is difficult because the skills required to explore are fundamentally opposed to those required to exploit. In this article, I describe how difficult this leap between exploration and exploitation can be. I show that the move between R&D‐based exploration and exploitation is related to organizational failure. In addition, firms that are superior learners are more likely to survive the leap from exploitation to exploration, and firms that are not cutting R&D expenditure to manipulate earnings are more likely to survive the leap from exploration to exploitation. Copyright © 2015 John Wiley & Sons, Ltd.

Computing genus $1$ Jacobi forms

We develop an algorithm to compute Fourier expansions of vector valued modular forms for Weil representations. As an application, we compute explicit linear equivalences of special divisors on modular varieties of orthogonal type. We define three families of Hecke operators for Jacobi forms, and analyze the induced action on vector valued modular forms. The newspaces attached to one of these families are used to give a more memory efficient version of our algorithm. - See more at: http://www.ams.org/journals/mcom/2016-85-298/S0025-5718-2015-02992-5/#sthash.bv7cxz8N.dpuf

Excited Young diagrams, equivariant $K$-theory, and Schubert varieties

We give combinatorial descriptions of the restrictions to T-fixed points of the classes of structure sheaves of Schubert varieties in the T-equivariant K-theory of Grassmannians and of maximal isotropic Grassmannians of orthogonal and symplectic types. We also give formulas, based on these descriptions, for the Hilbert series and Hilbert polynomials at T-fixed points of the corresponding Schubert varieties. These descriptions and formulas are given in terms of two equivalent combinatorial models: excited Young diagrams and set-valued tableaux. The restriction fomulas are positive, in that for a Schubert variety of codimension d, the formula equals (-1)^d times a sum, with nonnegative coefficients, of monomials in the expressions (e^{-\alpha}-1), as \alpha runs over the positive roots. In types A_n and C_n the restriction formulas had been proved earlier by [Kreiman 05], [Kreiman 06] by a different method. In type A_n, the formula for the Hilbert series had been proved earlier by [Li-Yong 12]. The method of this paper, which relies on a restriction formula of [Graham 02] and [Willems 06], is based on the method used by [Ikeda-Naruse 09] to obtain the analogous formulas in equivariant cohomology. The formulas we give differ from the K-theoretic restriction formulas given by [Ikeda-Naruse 11], which use different versions of excited Young diagrams and set-valued tableaux. We also give Hilbert series and Hilbert polynomial formulas which are valid for Schubert varieties in any cominuscule flag variety, in terms of the 0-Hecke algebra.

Supramolecular amphipathicity for probing antimicrobial propensity of host defence peptides.

Host defence peptides (HDPs) are effector components of innate immunity that provide defence against pathogens. These are small-to-medium sized proteins which fold into amphipathic conformations toxic to microbial membranes. Here we explore the concept of supramolecular amphipathicity for probing antimicrobial propensity of HDPs using elementary HDP-like amphiphiles. Such amphiphiles are individually inactive, but when ordered into microscopic micellar assemblies, respond to membrane binding according to the orthogonal type of their primary structure. The study demonstrates that inducible supramolecular amphipathicity can discriminate against bacterial growth and colonisation thereby offering a physico-chemical rationale for tuneable targeting of biological membranes.

Supercharacters of unipotent groups defined by involutions

We construct supercharacter theories of finite unipotent groups in the orthogonal, symplectic and unitary types. Our method utilizes group actions in a manner analogous to that of Diaconis and Isaacs in their construction of supercharacters of algebra groups. The resulting supercharacter theories agree with those of André and Neto in the case of the unipotent orthogonal and symplectic groups and generalize to a large collection of subgroups. In the unitary group case, we describe the supercharacters and superclasses in terms of labeled set partitions and calculate the supercharacter table.

The Tate conjecture for K3 surfaces in odd characteristic

We show that the classical Kuga–Satake construction gives rise, away from characteristic $$2$$ , to an open immersion from the moduli of primitively polarized K3 surfaces (of any fixed degree) to a certain regular integral model for a Shimura variety of orthogonal type. This allows us to attach to every polarized K3 surface in odd characteristic an abelian variety such that divisors on the surface can be identified with certain endomorphisms of the attached abelian variety. In turn, this reduces the Tate conjecture for K3 surfaces over finitely generated fields of odd characteristic to a version of the Tate conjecture for certain endomorphisms on the attached Kuga–Satake abelian variety, which we prove. As a by-product of our methods, we also show that the moduli stack of primitively polarized K3 surfaces of degree $$2d$$ is quasi-projective and, when $$d$$ is not divisible by $$p^2$$ , is geometrically irreducible in characteristic $$p$$ . We indicate how the same method applies to prove the Tate conjecture for co-dimension $$2$$ cycles on cubic fourfolds.

Recent improvement of a FIB-SEM serial-sectioning method for precise 3D image reconstruction - application of the orthogonally-arranged FIB-SEM.

IntroductionWe installed the first "orthogonally-arranged" FIB-SEM in 2011. The most characteristic point of this instrument is that the FIB and SEM columns are perpendicularly mounted; this is specially designed to obtain a serial-sectioning dataset more accurately and precisely with higher contrast and higher spatial resolution compare to other current FIB-SEMs [1]. Since the installation in 2011, we have developed the hardware and methodology of the serial-sectioning based on this orthogonal FIB-SEM. In order to develop this technique, we have widely opened this instrument to every researcher of all fields. In the presentation, I would like to introduce some of application results that are obtained by users of this instrument. The characteristic points of the orthogonal systemFigure1 shows a difference between the standard and the orthogonal FIB-SEM systems: In the standard system, shown in Fig.1(a), optical axes of a FIB and a SEM crosses around 60deg., while in the orthogonal system (Fig.1(b)), they are perpendicular to each other. The standard arrangement (a) is certainly suitable for TEM lamellae preparation etc. because the FIB and the SEM can see the same position simultaneously. However, for a serial-sectioning, it is not to say the best arrangement. One of the reasons is that the sliced plane by the FIB is not perpendicular to the electron beam so that the background contrast is not uniform and observed plane is distorted. On the other hand, in case of the orthogonally-arranged system,(b), these problems are resolved. In addition, spatial resolution can keep high enough even in a low accelerating voltage (e.g. 500V) because a working distance is set very small, 2mm. From these special design, we can obtain the serial-sectioning dataset from rather wide area (∼100um) with high spatial resolution (Max. 2×2×2nm). As this system has many kinds of detectors: SE, ET, Backscatter Electron(Energy-selective), EDS, EBSD, STEM(BF&ADF), with Ar+ ion-gun and a plasma cleaner, many kinds of signals can be obtained simultaneously.jmicro;63/suppl_1/i5-a/DFU077F1F1DFU077F1Fig. 1.Schematic illustration described (a) a standard type arrangement, (b) an orthogonal type arrangement. Recent topics and Future prospectsWe have applied this instrument for wide area of microstructure analysis; Metals and Alloys, Semiconductor devices, Battery electrodes, Minerals, Biomaterials, and so on. In my presentation, I would like to introduce some of our application results and will discuss about future development of the methodology of a FIB-SEM serial sectioning. As the applied research field becomes wider, various requests for the method were arisen. However, most requests can be summarized as follows: observation of larger area, expansion of applicable sample, obtain many kind of information, linkage with other instruments. AcknowledgmentsThe instrument introduced in this work was installed at NIMS by a part of "Low-carbon research network Japan" funded by the MEXT,Japan.

Designing hybrid onconase nanocarriers for mesothelioma therapy: a Taguchi orthogonal array and multivariate component driven analysis.

Onconase (ONC) is a member of a ribonuclease superfamily that has cytostatic activity against malignant mesothelioma (MM). The objective of this investigation was to develop bovine serum albumin (BSA)-chitosan based hybrid nanoformulations for the efficient delivery of ONC to MM while minimizing the exposure to normal tissues. Taguchi orthogonal array L9 type design was used to formulate ONC loaded BSA nanocarriers (ONC-ANC) with a mean particle size of 15.78 ± 0.24 nm (ζ = -21.89 ± 0.11 mV). The ONC-ANC surface was hybridized using varying chitosan concentrations ranging between 0.100 and 0.175% w/v to form various ONC loaded hybrid nanocarriers (ONC-HNC). The obtained data set was analyzed by principal component analysis (PCA) and principal component regressions (PCR) to decode the effects of investigated design variables. PCA showed positive correlations between investigated design variables like BSA, ethanol dilution, and total ethanol with particle size and entrapment efficiency (EE) of formulated nanocarriers. PCR showed that the particle size depends on BSA, ethanol dilution, and total ethanol content, while EE was only influenced by BSA content. Further analysis of chitosan and TPP effects used for coating of ONC-ANC by PCR confirmed their positive impacts on the particle size, zeta potential, and prolongation of ONC release compared to uncoated ONC-ANC. PCR analysis of preliminary stability studies showed increase in the particle size and zeta potential at lower pH. However, particle size, zeta potential, and EE of developed HNC were below 63 nm, 31 mV, and 96%, respectively, indicating their stability under subjected buffer conditions. Out of the developed formulations, HNC showed enhanced inhibition of cell viability with lower IC50 against human MM-REN cells compared to ONC and ONC-ANC. This might be attributed to the better cell uptake of HNC, which was confirmed in the cell uptake fluorescence studies. These studies indicated that a developed nanotherapeutic approach might aid in reducing the therapeutic dose of ONC, minimizing adverse effects by limiting the exposure of ONC to normal tissues, and help in the development of new therapeutic forms and routes of administration.

Découverte d’une industrie du Paléolithique inférieur en bordure de la commune de Nice, au Vallon obscur à Saint-Isidore

An archaic lithic assemblage has just been brought to light in border of the municipality of Nice (Alpes-Maritimes, France), in secondary position in a geologic context of middle fluviatile terrace in left bank of the Var. Lithic artefacts collected gather some shaping products (worked or broken pebbles) and débitage products (cores, flakes, angular fragments), obtained on pebbles mainly in marly limestone, stemming from the local plio-Pleistocene conglomerate and the alluviums of the Var. This lithic production shows essentially the beginnings of chaînes opératoires, with the first phases of pebbles cortex removing. Flakes are very mainly cortical or semi-cortical, and cores reveal a weak technical investment, with a reduced enough number of removal negatives. The débitage of orthogonal type is the most frequent, and the bipolar technique on anvil is attested. Some rare flakes are retouched by notches or by abrupt continuous retouches. The sector where was brought to light this lithic industry, in sediments reshaped below a level of fluviatile terrace of the Var in 70m of height, made us suggest a very ancient age for these vestiges, being able to go back up at the beginning of Middle Pleistocene, even of Lower Pleistocene, what is in agreement with the technical characteristics noticed on this lithic assemblage.

Burgers equation with time-dependent coefficients and nonlinear forcing term: Linearization and exact solvability

We construct and discuss a linearization method for solving Burgers equation with time-dependent coefficients and a nonlinear forcing term. Our results are shown to contain and generalize recent findings (Miskinis, 2001; Buyukasik and Pashaev, 2013). As applications of our method we solve several initial- and boundary-value problems for Burgers equation with forcing of sinusoidal, polynomial, as well as X1-Laguerre exceptional orthogonal polynomial type.

A Neurodynamic Optimization Method for Recovery of Compressive Sensed Signals With Globally Converged Solution Approximating to l0 Minimization.

Finding the optimal solution to the constrained l0 -norm minimization problems in the recovery of compressive sensed signals is an NP-hard problem and it usually requires intractable combinatorial searching operations for getting the global optimal solution, unless using other objective functions (e.g., the l1 norm or lp norm) for approximate solutions or using greedy search methods for locally optimal solutions (e.g., the orthogonal matching pursuit type algorithms). In this paper, a neurodynamic optimization method is proposed to solve the l0 -norm minimization problems for obtaining the global optimum using a recurrent neural network (RNN) model. For the RNN model, a group of modified Gaussian functions are constructed and their sum is taken as the objective function for approximating the l0 norm and for optimization. The constructed objective function sets up a convexity condition under which the neurodynamic system is guaranteed to obtain the globally convergent optimal solution. An adaptive adjustment scheme is developed for improving the performance of the optimization algorithm further. Extensive experiments are conducted to test the proposed approach in this paper and the output results validate the effectiveness of the new method.

Biot-Savart helicity versus physical helicity: A topological description of ideal flows

For an isentropic (thus compressible) flow, fluid trajectories are considered as orbits of a family of one parameter, smooth, orientation-preserving, and nonsingular diffeomorphisms on a compact and smooth-boundary domain in the Euclidian 3-space which necessarily preserve a finite measure, later interpreted as the fluid mass. Under such diffeomorphisms the Biot-Savart helicity of the pushforward of a divergence-free and tangent to the boundary vector field is proved to be conserved and since these circumstances present an isentropic flow, the conservation of the “Biot-Savart helicity” is established for such flows. On the other hand, the well known helicity conservation in ideal flows which here we call it “physical helicity” is found to be an independent constant with respect to the Biot-Savart helicity. The difference between these two helicities reflects some topological features of the domain as well as the velocity and vorticity fields which is discussed and is shown for simply connected domains the two helicities coincide. The energy variation of the vorticity field is shown to be formally the same as for the incompressible flow obtained before. For fluid domains consisting of several disjoint solid tori, at each time, the harmonic knot subspace of smooth vector fields on the fluid domain is found to have two independent base sets with a special type of orthogonality between these two bases by which a topological description of the vortex and velocity fields depending on the helicity difference is achieved since this difference is shown to depend only on the harmonic knot parts of velocity, vorticity, and its Biot-Savart vector field. For an ideal magnetohydrodynamics (MHD) flow three independent constant helicities are reviewed while the helicity of magnetic potential is generalized for non-simply connected domains by inserting a special harmonic knot field in the dynamics of the magnetic potential. It is proved that the harmonic knot part of the vorticity in hydrodynamics and the magnetic field in MHD is presented by constant coefficients (fluxes) when expanded in terms of one of the time dependent base functions.