L1\mathcal{L}^1 limit solutions for control systems

For a control Cauchy problem $$\dot x= {f}(t,x,u,v) +\sum_{\alpha=1}^m g_\alpha(x) \dot u_\alpha,\quad x(a)=\bar x,$$ on an interval $[a,b]$, we propose a notion of limit solution $x,$ verifying the following properties: i) $x$ is defined for $\mathcal{L}^1$ (impulsive) inputs $u$ and for standard, bounded measurable, controls $v$; ii) in the commutative case (i.e. when $[g_{\alpha},g_{\beta}]\equiv 0,$ for all $\alpha,\beta=1,...,m$), $x$ coincides with the solution one can obtain via the change of coordinates that makes the $g_\alpha$ simultaneously constant; iii) $x$ subsumes former concepts of solution valid for the generic, noncommutative case. In particular, when $u$ has bounded variation, we investigate the relation between limit solutions and (single-valued) graph completion solutions. Furthermore, we prove consistency with the classical Carath\'eodory solution when $u$ and $x$ are absolutely continuous. Even though some specific problems are better addressed by means of special representations of the solutions, we believe that various theoretical issues call for a unified notion of trajectory. For instance, this is the case of optimal control problems, possibly with state and endpoint constraints, for which no extra assumptions (like e.g. coercivity, bounded variation, commutativity) are made in advance

New magnetic phase in metallic V_{2-y}O_3 close to the metal insulator transition

We have observed two spin density wave (SDW) phases in hole doped metallic V_{2-y}O_3, one evolves from the other as a function of doping, pressure or temperature. They differ in their response to an external magnetic field, which can also induce a transition between them. The phase boundary between these two states in the temperature-, doping-, and pressure-dependent phase diagram has been determined by magnetization and magnetotransport measurements. One phase exists at high doping level and has already been described in the literature. The second phase is found in a small parameter range close to the boundary to the antiferromagnetic insulating phase (AFI). The quantum phase transitions between these states as a function of pressure and doping and the respective metamagnetic behavior observed in these phases are discussed in the light of structurally induced changes of the band structure.Comment: REVTeX, 8 pages, 12 EPS figures, submitted to PR

Hyperferritinemia and hypergammaglobulinemia predict the treatment response to standard therapy in autoimmune hepatitis.

Autoimmune hepatitis (AIH) is a chronic hepatitis with an increasing incidence. The majority of patients require life-long immunosuppression and incomplete treatment response is associated with a disease progression. An abnormal iron homeostasis or hyperferritinemia is associated with worse outcome in other chronic liver diseases and after liver transplantation. We assessed the capacity of baseline parameters including the iron status to predict the treatment response upon standard therapy in 109 patients with untreated AIH type 1 (AIH-1) in a retrospective single center study. Thereby, a hyperferritinemia (> 2.09 times upper limit of normal; Odds ratio (OR) = 8.82; 95% confidence interval (CI): 2.25-34.52) and lower immunoglobulins (<1.89 times upper limit of normal; OR = 6.78; CI: 1.87-24.59) at baseline were independently associated with the achievement of complete biochemical remission upon standard therapy. The predictive value increased when both variables were combined to a single treatment response score, when the cohort was randomly split into a training (area under the curve (AUC) = 0.749; CI 0.635-0.863) and internal validation cohort (AUC = 0.741; CI 0.558-0.924). Patients with a low treatment response score (<1) had significantly higher cumulative remission rates in the training (p<0.001) and the validation cohort (p = 0.024). The baseline hyperferritinemia was accompanied by a high serum iron, elevated transferrin saturations and mild hepatic iron depositions in the majority of patients. However, the abnormal iron status was quickly reversible under therapy. Mechanistically, the iron parameters were not stringently related to a hepatocellular damage. Ferritin rather seems deregulated from the master regulator hepcidin, which was down regulated, potentially mediated by the elevated hepatocyte growth factor. In conclusion, baseline levels of serum ferritin and immunoglobulins, which are part of the diagnostic work-up of AIH, can be used to predict the treatment response upon standard therapy in AIH-1, although confirmation from larger multicenter studies is pending

Magnetic correlations and quantum criticality in the insulating antiferromagnetic, insulating spin liquid, renormalized Fermi liquid, and metallic antiferromagnetic phases of the Mott system V_2O_3

Magnetic correlations in all four phases of pure and doped vanadium sesquioxide V_2O_3 have been examined by magnetic thermal neutron scattering. While the antiferromagnetic insulator can be accounted for by a Heisenberg localized spin model, the long range order in the antiferromagnetic metal is an incommensurate spin-density-wave, resulting from a Fermi surface nesting instability. Spin dynamics in the strongly correlated metal are dominated by spin fluctuations in the Stoner electron-hole continuum. Furthermore, our results in metallic V_2O_3 represent an unprecedentedly complete characterization of the spin fluctuations near a metallic quantum critical point, and provide quantitative support for the SCR theory for itinerant antiferromagnets in the small moment limit. Dynamic magnetic correlations for energy smaller than k_BT in the paramagnetic insulator carry substantial magnetic spectral weight. However, the correlation length extends only to the nearest neighbor distance. The phase transition to the antiferromagnetic insulator introduces a sudden switching of magnetic correlations to a different spatial periodicity which indicates a sudden change in the underlying spin Hamiltonian. To describe this phase transition and also the unusual short range order in the paramagnetic state, it seems necessary to take into account the orbital degrees of freedom associated with the degenerate d-orbitals at the Fermi level in V_2O_3.Comment: Postscript file, 24 pages, 26 figures, 2 tables, accepted by Phys. Rev.

Proximal Analysis and the Minimal Time Function of a Class of Semilinear Control Systems

The minimal time function of a class of semilinear control systems is considered in Banach spaces, with the target set being a closed ball. It is shown that the minimal time functions of the Yosida approximation equations converge to the minimal time function of the semilinear control system. Complete characterization is established for the subdifferential of the minimal time function satisfying the Hamilton–Jacobi–Bellman equation. These results extend the theory of finite dimensional linear control systems to infinite dimensional semilinear control systems

Helical spin-density wave in doped V2O3

Recent neutron scattering and nuclear magnetic resonance experiments have revealed that the low temperature phase of doped V_{2-y}O_3 is an itinerant antiferromagnet with a helical spin structure. We use a band structure calculation as the point of departure to show that these experiments are in agreement with mean field results for an Overhauser spin-density wave state. The influences of a finite life-time and of dilute magnetic impurities are discussed.Comment: 6 pages RevTex incl. 7 postscript figures, to be published by PR

Regularity of a kind of marginal functions in Hilbert spaces

We study well-posedness of some mathematical programming problem depending on a parameter that generalizes in a certain sense the metric projection onto a closed nonconvex set. We are interested in regularity of the set of minimizers as well as of the value function, which can be seen, on one hand, as the viscosity solution to a Hamilton-Jacobi equation, while, on the other, as the minimal time in some related optimal time control problem. The regularity includes both the Fréchet differentiability of the value function and the Hölder continuity of its (Fréchet) gradient

Two Alleles of NF-κB in the Sea Anemone Nematostella vectensis Are Widely Dispersed in Nature and Encode Proteins with Distinct Activities

BACKGROUND. NF-κB is an evolutionarily conserved transcription factor that controls the expression of genes involved in many key organismal processes, including innate immunity, development, and stress responses. NF-κB proteins contain a highly conserved DNA-binding/dimerization domain called the Rel homology domain. METHODS/PRINCIPAL FINDINGS. We characterized two NF-κB alleles in the sea anemone Nematostella vectensis that differ at nineteen single-nucleotide polymorphisms (SNPs). Ten of these SNPs result in amino acid substitutions, including six within the Rel homology domain. Both alleles are found in natural populations of Nematostella. The relative abundance of the two NF-κB alleles differs between populations, and departures from Hardy-Weinberg equilibrium within populations indicate that the locus may be under selection. The proteins encoded by the two Nv-NF-κB alleles have different molecular properties, in part due to a Cys/Ser polymorphism at residue 67, which resides within the DNA recognition loop. In nearly all previously characterized NF-κB proteins, the analogous residue is fixed for Cys, and conversion of human RHD proteins from Cys to Ser at this site has been shown to increase DNA-binding ability and increase resistance to inhibition by thiol-reactive compounds. However, the naturally-occurring Nematostella variant with Cys at position 67 binds DNA with a higher affinity than the Ser variant. On the other hand, the Ser variant activates transcription in reporter gene assays more effectively, and it is more resistant to inhibition by a thiol-reactive compound. Reciprocal Cys<->Ser mutations at residue 67 of the native Nv-NF-κB proteins affect DNA binding as in human NF-κB proteins, e.g., a Cys->Ser mutation increases DNA binding of the native Cys variant. CONCLUSIONS/SIGNIFICANCE. These results are the first demonstration of a naturally occurring and functionally significant polymorphism in NF-κB in any species. The functional differences between these alleles and their uneven distribution in the wild suggest that different genotypes could be favored in different environments, perhaps environments that vary in their levels of peroxides or thiol-reactive compounds.National Institutes of Health (CA047763); National Science Foundation (FP-91656101-0); Environmental Protection Agency (F5E11155); Conservation International Marine Management Area Science Program; Boston University (SPRInG grant); Postdoctoral Scholar Program at the Woods Hole Oceanographic Institution; The Beacon Institute for Rivers and Estuaries; the J Seward Johnson Fund; Boston University (5 P42 ES07381

CD83 Modulates B Cell Function In Vitro: Increased IL-10 and Reduced Ig Secretion by CD83Tg B Cells

The murine transmembrane glycoprotein CD83 is an important regulator for both thymic T cell maturation and peripheral T cell responses. Recently, we reported that CD83 also has a function on B cells: Ubiquitous transgenic (Tg) expression of CD83 interfered with the immunoglobulin (Ig) response to infectious agents and to T cell dependent as well as T cell independent model antigen immunization. Here we compare the function of CD83Tg B cells that overexpress CD83 and CD83 mutant (CD83mu) B cells that display a drastically reduced CD83 expression. Correlating with CD83 expression, the basic as well as the lipopolysaccharide (LPS) induced expression of the activation markers CD86 and MHC-II are significantly increased in CD83Tg B cells and reciprocally decreased in CD83mu B cells. Wild-type B cells rapidly upregulate CD83 within three hours post BCR or TLR engagement by de novo protein synthesis. The forced premature overexpression of CD83 on the CD83Tg B cells results in reduced calcium signaling, reduced Ig secretion and a reciprocally increased IL-10 production upon in vitro activation. This altered phenotype is mediated by CD83 expressed on the B cells themselves, since it is observed in the absence of accessory cells. In line with this finding, purified CD83mu B cells displayed a reduced IL-10 production and slightly increased Ig secretion upon LPS stimulation in vitro. Taken together, our data strongly suggest that CD83 is expressed by B cells upon activation and contributes to the regulation of B cell function