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The identities for elliptic gamma functions discovered by Felder and Varchenko [8] are generalized to an infinite set of identities for elliptic gamma functions associated to pairs of planes in 3-dimensional space. The language of...
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The identities for elliptic gamma functions discovered by Felder and Varchenko [8] are generalized to an infinite set of identities for elliptic gamma functions associated to pairs of planes in 3-dimensional space. The language of stacks and gerbes gives a natural framework for a systematic description of these identities and their domain of validity. A triptic curve is the quotient of the complex plane by a subgroup of rank three. (It is a stack.) Our identities can be summarized by saying that elliptic gamma functions form a meromorphic section of a hermitian holomorphic abelian gerbe over the universal oriented triptic curve.
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Rolling adhesion on vascular surfaces is the first step in recruiting circulating leukocytes, hematopoietic progenitors, or platelets to specific organs or to sites of infection or injury. Rolling requires the rapid yet balanced f...
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Rolling adhesion on vascular surfaces is the first step in recruiting circulating leukocytes, hematopoietic progenitors, or platelets to specific organs or to sites of infection or injury. Rolling requires the rapid yet balanced formation and dissociation of adhesive bonds in the challenging environment of blood flow. This review explores how structurally distinct adhesion receptors interact through mechanically regulated kinetics with their ligands to meet these challenges. Remarkably, increasing force applied to adhesive bonds first prolongs their lifetimes (catch bonds) and then shortens their lifetimes (slip bonds). Catch bonds mediate the counterintuitive phenomenon of flow-enhanced rolling adhesion. Force-regulated disruptions of receptor interdomain or intradomain interactions remote from the ligand-binding surface generate catch bonds. Adhesion receptor dimerization, clustering in membrane domains, and interactions with the cytoskeleton modulate the forces applied to bonds. Both inside-out and outside-in cell signals regulate these processes.
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Rolling adhesion on vascular surfaces is the first step in recruiting circulating leukocytes, hematopoietic progenitors, or platelets to specific organs or to sites of infection or injury. Rolling requires the rapid yet balanced f...
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Rolling adhesion on vascular surfaces is the first step in recruiting circulating leukocytes, hematopoietic progenitors, or platelets to specific organs or to sites of infection or injury. Rolling requires the rapid yet balanced formation and dissociation of adhesive bonds in the challenging environment of blood flow. This review explores how structurally distinct adhesion receptors interact through mechanically regulated kinetics with their ligands to meet these challenges. Remarkably, increasing force applied to adhesive bonds first prolongs their lifetimes (catch bonds) and then shortens their lifetimes (slip bonds). Catch bonds mediate the counterintuitive phenomenon of flow-enhanced rolling adhesion. Force-regulated disruptions of receptor interdomain or intradomain interactions remote from the ligand-binding surface generate catch bonds. Adhesion receptor dimerization, clustering in membrane domains, and interactions with the cytoskeleton modulate the forces applied to bonds. Both inside-out and outside-in cell signals regulate these processes.
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Based on the existence theory on the Boltzmann equation with external forces in infinite vacuum, in this paper, we will study the L-1 and BV-type stability of the classical solutions for small initial data. The stability results g...
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Based on the existence theory on the Boltzmann equation with external forces in infinite vacuum, in this paper, we will study the L-1 and BV-type stability of the classical solutions for small initial data. The stability results generalize those for the Boltzmann equation without force to the case with external force. In particular, we show that the stability can be established for the soft potentials directly, while the stability for the hard potentials and hard sphere model is obtained through the construction of some nonlinear functionals. The functionals thus constructed generalize those constructed in [S.-Y. Ha, Nonlinear functionals of the Boltzmann equation and uniform stability estimates, J. Differential Equations 215 (2005) 178-205] for the case without force to capture the effect of the force term on the time evolution of the solutions. (c) 2006 Elsevier Inc. All rights reserved.
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In response to the increasing needs for control and optimization of hybrid systems, this work is concerned with such asymptotic properties as recurrence (also known as weak stochastic stability in the literature) and ergodicity of...
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In response to the increasing needs for control and optimization of hybrid systems, this work is concerned with such asymptotic properties as recurrence (also known as weak stochastic stability in the literature) and ergodicity of regime-switching diffusions. Using Liapunov functions, necessary and sufficient conditions for positive recurrence are developed. Then, ergodicity of positive recurrent regime-switching diffusions is obtained by constructing cycles using the associated discretetime Markov chains.
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We introduce a notion of "hopfish algebra" structure on an associative algebra, allowing the structure morphisms (coproduct, counit, antipode) to be bimodules rather than algebra homomorphisms. We prove that quasi-Hopf algebras ar...
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We introduce a notion of "hopfish algebra" structure on an associative algebra, allowing the structure morphisms (coproduct, counit, antipode) to be bimodules rather than algebra homomorphisms. We prove that quasi-Hopf algebras are hopfish algebras. We find that a hopfish structure on the algebra of functions on a finite set G is closely related to a "hypergroupoid" structure on G. The Morita theory of hopfish algebras is also discussed.
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Interleukin-12 receptor beta1 (IL-12Rbeta1) deficiency is the most common form of Mendelian susceptibility to mycobacterial disease (MSMD). We undertook an international survey of 141 patients from 102 kindreds in 30 countries. Am...
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Interleukin-12 receptor beta1 (IL-12Rbeta1) deficiency is the most common form of Mendelian susceptibility to mycobacterial disease (MSMD). We undertook an international survey of 141 patients from 102 kindreds in 30 countries. Among 102 probands, the first infection occurred at a mean age of 2.4 years. In 78 patients, this infection was caused by Bacille Calmette-Guerin (BCG; n = 65), environmental mycobacteria (EM; also known as atypical or nontuberculous mycobacteria) (n = 9) or Mycobacterium tuberculosis (n = 4). Twenty-two of the remaining 24 probands initially presented with nontyphoidal, extraintestinal salmonellosis. Twenty of the 29 genetically affected sibs displayed clinical signs (69%); however 8 remained asymptomatic (27%). Nine nongenotyped sibs with symptoms died. Recurrent BCG infection was diagnosed in 15 cases, recurrent EM in 3 cases, recurrent salmonellosis in 22 patients. Ninety of the 132 symptomatic patients had infections with a single microorganism. Multiple infections were diagnosed in 40 cases, with combined mycobacteriosis and salmonellosis in 36 individuals. BCG disease strongly protected against subsequent EM disease (p = 0.00008). Various other infectious diseases occurred, albeit each rarely, yet candidiasis was reported in 33 of the patients (23%). Ninety-nine patients (70%) survived, with a mean age at last follow-up visit of 12.7 years +/- 9.8 years (range, 0.5-46.4 yr). IL-12Rbeta1 deficiency is characterized by childhood-onset mycobacteriosis and salmonellosis, rare recurrences of mycobacterial disease, and more frequent recurrence of salmonellosis. The condition has higher clinical penetrance, broader susceptibility to infections, and less favorable outcome than previously thought.
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Based on the global existence theory of the Vlasov-Poisson-Boltzmann system around vacuum in the N-dimensional phase space, in this paper, we prove the uniform L-1 stability of classical solutions for small initial data when N >= ...
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Based on the global existence theory of the Vlasov-Poisson-Boltzmann system around vacuum in the N-dimensional phase space, in this paper, we prove the uniform L-1 stability of classical solutions for small initial data when N >= 4. In particular, we show that the stability can be established directly for the soft potentials, while for the hard potentials and hard sphere model it is obtained through the construction of some nonlinear functionals. These functionals thus generalize those constructed by Ha for the case without force to capture the effect of the force term on the time evolution of solutions. In addition, the local-in-time L-1 stability is also obtained for the case of N = 3.
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The objective of this review is to provide basic information pertaining to biomechanical aspects of bone as they relate to tissue engineering. The review is written for the general tissue engineering reader, who may not have a bio...
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The objective of this review is to provide basic information pertaining to biomechanical aspects of bone as they relate to tissue engineering. The review is written for the general tissue engineering reader, who may not have a biomechanical engineering background. To this end, biomechanical characteristics and properties of normal and repair cortical and cancellous bone are presented. Also, this chapter intends to describe basic structure-function relationships of these two types of bone. Special emphasis is placed on salient classical and modern testing methods, with both material and structural properties described.
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Lymphocyte maturation requires generation of a large diversity of antigen receptors, which involves somatic rearrangements at the antigen receptor genes in a process termed V(D)J recombination. Upon encountering specific antigens,...
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Lymphocyte maturation requires generation of a large diversity of antigen receptors, which involves somatic rearrangements at the antigen receptor genes in a process termed V(D)J recombination. Upon encountering specific antigens, B-lymphocytes undergo rearrangements in the constant region of the immunoglobulin genes to optimize immune responses in a process called class switch recombination. Activated B-cells also undergo somatic hypermutation in the variable regions of the immunoglobulin genes to enhance their antigenic affinity. These somatic events are initiated by the infliction of DNA lesions within the antigen receptor genes that are strictly confined to a specific developmental window and cell-cycle stage. DNA lesions are then repaired by one of the general DNA repair mechanisms, such as non-homologous end-joining. Mutations in key factors of these pathways lead to the interruption of these processes and immunodeficiency, making it possible to study the mechanisms of cellular response to DNA lesions and their repair. This review briefly summarizes some of the recently developed animal models with focus on current advances in the understanding of the mechanism of DNA end-joining activities, and its role in the maintenance of genomic stability and the prevention of tumorigenesis.
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