Nonabelian Jacobian of smooth projective surface : a survey

The nonabelian Jacobian J(X; L, d) of a smooth projective surface X is inspired by the classical theory of Jacobian of curves. It is built as a natural scheme interpolating between the Hilbert scheme X [d] of subschemes of length d of X and the stack M X (2, L, d) of torsion free sheaves of rank 2 on X having the determinant O X (L) and the second Chern class (= number) d. It relates to such influential ideas as variations of Hodge structures, period maps, nonabelian Hodge theory, Homological mirror symmetry, perverse sheaves, geometric Langlands program. These relations manifest themselves by the appearance of the following structures on J(X; L, d): a sheaf of reductive Lie algebras (singular) Fano toric varieties whose hyperplane sections are (singular) Calabi-Yau varieties trivalent graphs. This is an expository paper giving an account of most of the main properties of J(X; L, d) uncovered in Reider 2006 and ArXiv:1103.4794v1

Nonabelian Jacobian of Projective Surfaces : Geometry and Representation Theory

The Jacobian of a smooth projective curve is undoubtedly one of the most remarkable and beautiful objects in algebraic geometry. This work is an attempt to develop an analogous theory for smooth projective surfaces - a theory of the nonabelian Jacobian of smooth projective surfaces. Just like its classical counterpart, our nonabelian Jacobian relates to vector bundles (of rank 2) on a surface as well as its Hilbert scheme of points. But it also comes equipped with the variation of Hodge-like structures, which produces a sheaf of reductive Lie algebras naturally attached to our Jacobian. This constitutes a nonabelian analogue of the (abelian) Lie algebra structure of the classical Jacobian. This feature naturally relates geometry of surfaces with the representation theory of reductive Lie algebras/groups. This work’s main focus is on providing an in-depth study of various aspects of this relation. It presents a substantial body of evidence that the sheaf of Lie algebras on the nonabelian Jacobian is an efficient tool for using the representation theory to systematically address various algebro-geometric problems. It also shows how to construct new invariants of representation theoretic origin on smooth projective surfaces

MRI Parameters Of Alzheimer's Disease in an Arab Population of Wadi Ara, Israel

Magnetic resonance imaging (MRI) findings are reported from 15 individuals in an Arab–Israeli community who were diagnosed with Alzheimer's disease (AD). The quantitative parameters that were used for MRI analyses included gradings (0–3) and linear measurements of different brain structures. Generalized tissue loss was assessed by combined measurements of the ventricles (ventricular score, VS) and sulcal grading and width (SG, SW, respectively). Loss of brain tissue in specific regions of interest, eg, temporal lobes, basal ganglia, and midbrain, was evaluated by precise measurements. We observed abnormal tissue characteristics, expressed as high intensity foci in white matter on T2W sequences, as well as tissue loss, both generalized and focal. Most notable were changes involving the head of the caudate nuclei, the midbrain, and to a lesser degree, medial temporal structures.National Institute of Aging (UO1-AG17173); National Institute on Alcohol Abuse and Alcoholism (R37-AA07112, K05-AA00219); US Department of Veterans Affair

Characterization of the 4-canonical birationality of algebraic threefolds

In this article we present a 3-dimensional analogue of a well-known theorem of E. Bombieri (in 1973) which characterizes the bi-canonical birationality of surfaces of general type. Let $X$ be a projective minimal 3-fold of general type with $\mathbb{Q}$-factorial terminal singularities and the geometric genus $p_g(X)\ge 5$. We show that the 4-canonical map $\phi_4$ is {\it not} birational onto its image if and only if $X$ is birationally fibred by a family $\mathscr{C}$ of irreducible curves of geometric genus 2 with $K_X\cdot C_0=1$ where $C_0$ is a general irreducible member in $\mathscr{C}$.Comment: 25 pages, to appear in Mathematische Zeitschrif

Anti-Pluricanonical Systems On Q-Fano Threefolds

We investigate birationality of the anti-pluricanonical map $\phi_{-m}$, the rational map defined by the anti-pluricanonical system $|-mK|$, on $\mathbb{Q}$-Fano threefolds.Comment: 18 page

On complex surfaces diffeomorphic to rational surfaces

In this paper we prove that no complex surface of general type is diffeomorphic to a rational surface, thereby completing the smooth classification of rational surfaces and the proof of the Van de Ven conjecture on the smooth invariance of Kodaira dimension.Comment: 34 pages, AMS-Te

Atomic excitation during recollision-free ultrafast multi-electron tunnel ionization

Modern intense ultrafast pulsed lasers generate an electric field of sufficient strength to permit tunnel ionization of the valence electrons in atoms. This process is usually treated as a rapid succession of isolated events, in which the states of the remaining electrons are neglected. Such electronic interactions are predicted to be weak, the exception being recollision excitation and ionization caused by linearly-polarized radiation. In contrast, it has recently been suggested that intense field ionization may be accompanied by a two-stage `shake-up' reaction. Here we report a unique combination of experimental techniques that enables us to accurately measure the tunnel ionization probability for argon exposed to 50 femtosecond laser pulses. Most significantly for the current study, this measurement is independent of the optical focal geometry, equivalent to a homogenous electric field. Furthermore, circularly-polarized radiation negates recollision. The present measurements indicate that tunnel ionization results in simultaneous excitation of one or more remaining electrons through shake-up. From an atomic physics standpoint, it may be possible to induce ionization from specific states, and will influence the development of coherent attosecond XUV radiation sources. Such pulses have vital scientific and economic potential in areas such as high-resolution imaging of in-vivo cells and nanoscale XUV lithography.Comment: 17 pages, 4 figures, original format as accepted by Nature Physic

Low unesterified:esterified eicosapentaenoic acid (EPA) plasma concentration ratio is associated with bipolar disorder episodes, and omega‐3 plasma concentrations are altered by treatment

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/115916/1/bdi12337_am.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/115916/2/bdi12337.pd

Corporate Social Responsibility/Sustainability Reporting Among the Fortune Global 250: Greenwashing or Green Supply Chain?

The sustainability reporting efforts of MNCs who are members of the Fortune Global 250 (FG250) was investigated. The focus was on sustainability reporting by MNCs of supply chain impacts. The reporting of FG250 MNCs was examined to determine if greenwashing was occurring or whether MNCs had committed to operating a green supply chain. A mixed methodology was used consisting of quantitative analysis of twenty-five MNC CSR/sustainability reports which were randomly selected from the FG250 listing. Qualitative analysis using content analysis was also conducted on the reports. Both methodologies concentrated on the sustainability reporting of the selected MNCs in regard to their supply chain. Findings were mixed as there were great variations among the MNCs in their level of sustainability reporting about their supply chains. Some MNCs did not report on the activities of their supply chain at all (20%), the majority of the MNCs reported on their supply chain impacts at the value and goal level (48%), while the rest reported at the management approach level (32%). A majority of the sampled MNCs could be accused of greenwashing due to the lack of detailed quantitative information provided by the MNCs on the environmental impacts of their supply chai

Structural Disorder Provides Increased Adaptability for Vesicle Trafficking Pathways

Vesicle trafficking systems play essential roles in the communication between the organelles of eukaryotic cells and also between cells and their environment. Endocytosis and the late secretory route are mediated by clathrin-coated vesicles, while the COat Protein I and II (COPI and COPII) routes stand for the bidirectional traffic between the ER and the Golgi apparatus. Despite similar fundamental organizations, the molecular machinery, functions, and evolutionary characteristics of the three systems are very different. In this work, we compiled the basic functional protein groups of the three main routes for human and yeast and analyzed them from the structural disorder perspective. We found similar overall disorder content in yeast and human proteins, confirming the well-conserved nature of these systems. Most functional groups contain highly disordered proteins, supporting the general importance of structural disorder in these routes, although some of them seem to heavily rely on disorder, while others do not. Interestingly, the clathrin system is significantly more disordered (,23%) than the other two, COPI (,9%) and COPII (,8%). We show that this structural phenomenon enhances the inherent plasticity and increased evolutionary adaptability of the clathrin system, which distinguishes it from the other two routes. Since multi-functionality (moonlighting) is indicative of both plasticity and adaptability, we studied its prevalence in vesicle trafficking proteins and correlated it with structural disorder. Clathrin adaptors have the highest capability for moonlighting while also comprising the most highly disordered members. The ability to acquire tissue specific functions was also used to approach adaptability: clathrin route genes have the most tissue specific exons encoding for protein segments enriched in structural disorder and interaction sites. Overall, our results confirm the general importance of structural disorder in vesicle trafficking and suggest major roles for this structural property in shaping the differences of evolutionary adaptability in the three routes