Combinatorial Hopf algebras and Towers of Algebras

Bergeron and Li have introduced a set of axioms which guarantee that the Grothendieck groups of a tower of algebras $\bigoplus_{n\ge0}A_n$ can be endowed with the structure of graded dual Hopf algebras. Hivert and Nzeutzhap, and independently Lam and Shimozono constructed dual graded graphs from primitive elements in Hopf algebras. In this paper we apply the composition of these constructions to towers of algebras. We show that if a tower $\bigoplus_{n\ge0}A_n$ gives rise to graded dual Hopf algebras then we must have $\dim(A_n)=r^nn!$ where $r = \dim(A_1)$.Comment: 7 page

Role of 1q21 in multiple myeloma: From pathogenesis to possible therapeutic targets

Multiple myeloma (MM) is characterized by an accumulation of malignant plasma cells (PCs) in the bone marrow (BM). The amplification of 1q21 is one of the most common cytogenetic abnormalities occurring in around 40% of de novo patients and 70% of relapsed/refractory MM. Patients with this unfavorable cytogenetic abnormality are considered to be high risk with a poor response to standard therapies. The gene(s) driving amplification of the 1q21 amplicon has not been fully studied. A number of clear candidates are under investigation, and some of them (IL6R, ILF2, MCL-1, CKS1B and BCL9) have been recently proposed to be potential drivers of this region. However, much remains to be learned about the biology of the genes driving the disease progression in MM patients with 1q21 amp. Understanding the mechanisms of these genes is important for the development of effective targeted therapeutic approaches to treat these patients for whom effective therapies are currently lacking. In this paper, we review the current knowledge about the pathological features, the mechanism of 1q21 amplification, and the signal pathway of the most relevant candidate genes that have been suggested as possible therapeutic targets for the 1q21 amplicon

Large Scale Optimization Problems for Central Energy Facilities with Distributed Energy Storage

On large campuses, energy facilities are used to serve the heating and cooling needs of all the buildings, while utilizing cost savings strategies to manage operational cost. Strategies range from shifting loads to participating in utility programs that offer payouts. Among available strategies are central plant optimization, electrical energy storage, participation in utility demand response programs, and manipulating the temperature setpoints in the campus buildings. However, simultaneously optimizing all of the central plant assets, temperature setpoints and participation in utility programs can be a daunting task even for a powerful computer if the desire is real time control. These strategies may be implemented separately across several optimization systems without a coordinating algorithm. Due to system interactions, decentralized control may be far from optimal and worse yet may try to use the same asset for different goals. In this work, a hierarchal optimization system has been created to coordinate the optimization of the central plant, the battery, participation in demand response programs, and temperature setpoints. In the hierarchal controller, the high level coordinator determines the load allocations across the campus or facility. The coordinator also determines the participation in utility incentive programs. It is shown that these incentive programs can be grouped into reservation programs and price adjustment programs. The second tier of control is split into 3 portions: control of the central energy facility, control of the battery system, and control of the temperature setpoints. The second tier is responsible for converting load allocations into central plant temperature setpoints and flows, battery charge and discharge setpoints, and temperature setpoints, which are delivered to the Building Automation System for execution. It is shown that the whole system can be coordinated by representing the second tier controllers with a smaller set of data that can be used by the coordinating controller. The central plant optimizer must supply an operational domain which constrains how each group of equipment can operate. The high level controller uses this information to send down loadings for each resource a group of equipment in the plant produces or consumes. For battery storage, the coordinating controller uses a simple integrator model of the battery and is responsible for providing a demand target and the amount of participation in any incentive programs. Finally, to perform temperature setpoint optimization a dynamic model of the zone is provided to the coordinating controller. This information is used to determine load allocations for groups of zones. The hierarchal control strategy is successful at optimizing the entire energy facility fast enough to allow the algorithms to control the energy facility, building setpoints, and program bids in real-time

Fermionic Coset, Critical Level W^(2)_4-Algebra and Higher Spins

The fermionic coset is a limit of the pure spinor formulation of the AdS5xS5 sigma model as well as a limit of a nonlinear topological A-model, introduced by Berkovits. We study the latter, especially its symmetries, and map them to higher spin algebras. We show the following. The linear A-model possesses affine \AKMSA{pgl}{4}{4}_0 symmetry at critical level and its \AKMSA{psl}{4}{4}_0 current-current perturbation is the nonlinear model. We find that the perturbation preserves $\mathcal{W}^{(2)}_4$-algebra symmetry at critical level. There is a topological algebra associated to \AKMSA{pgl}{4}{4}_0 with the properties that the perturbation is BRST-exact. Further, the BRST-cohomology contains world-sheet supersymmetric symplectic fermions and the non-trivial generators of the $\mathcal{W}^{(2)}_4$-algebra. The Zhu functor maps the linear model to a higher spin theory. We analyze its \SLSA{psl}{4}{4} action and find finite dimensional short multiplets.Comment: 25 page

q-Analogue of Am−1⊕An−1⊂Amn−1A_{m-1}\oplus A_{n-1}\subset A_{mn-1}

A natural embedding $A_{m-1}\oplus A_{n-1}\subset A_{mn-1}$ for the corresponding quantum algebras is constructed through the appropriate comultiplication on the generators of each of the $A_{m-1}$ and $A_{n-1}$ algebras. The above embedding is proved in their $q$-boson realization by means of the isomorphism between the $\mathcal{A}_q^{-}$ (mn)$\sim {\otimes} ^n \mathcal{A}_q^{-}$(m)$\sim {\otimes}^m\mathcal{A}_q^{-}$(n) algebras.Comment: 11 pages, no figures. In memory of professor R. P. Rousse

PD-L1/PD-1 Pattern of Expression Within the Bone Marrow Immune Microenvironment in Smoldering Myeloma and Active Multiple Myeloma Patients

Background: The PD-1/PD-L1 axis has recently emerged as an immune checkpoint that controls antitumor immune responses also in hematological malignancies. However, the use of anti-PD-L1/PD-1 antibodies in multiple myeloma (MM) patients still remains debated, at least in part because of discordant literature data on PD-L1/PD-1 expression by MM cells and bone marrow (BM) microenvironment cells. The unmet need to identify patients which could benefit from this therapeutic approach prompts us to evaluate the BM expression profile of PD-L1/PD-1 axis across the different stages of the monoclonal gammopathies. Methods: The PD-L1/PD-1 axis was evaluated by flow cytometry in the BM samples of a total cohort of 141 patients with monoclonal gammopathies including 24 patients with Monoclonal Gammopathy of Undetermined Significance (MGUS), 38 patients with smoldering MM (SMM), and 79 patients with active MM, including either newly diagnosed or relapsed-refractory patients. Then, data were correlated with the main immunological and clinical features of the patients. Results: First, we did not find any significant difference between MM and SMM patients in terms of PD-L1/PD-1 expression, on both BM myeloid (CD14+) and lymphoid subsets. On the other hand, PD-L1 expression by CD138+ MM cells was higher in both SMM and MM as compared to MGUS patients. Second, the analysis on the total cohort of MM and SMM patients revealed that PD-L1 is expressed at higher level in CD14+CD16+ non-classical monocytes compared with classical CD14+CD16− cells, independently from the stage of disease. Moreover, PD-L1 expression on CD14+ cells was inversely correlated with BM serum levels of the anti-tumoral cytokine, IL-27. Interestingly, relapsed MM patients showed an inverted CD4+/CD8+ ratio along with high levels of pro-tumoral IL-6 and a positive correlation between Í14+PD-L1+ and Í8+PD-1+ cells as compared to both SMM and newly diagnosed MM patients suggesting a highly compromised immune-compartment with low amount of CD4+ effector cells. Conclusions: Our data indicate that SMM and active MM patients share a similar PD-L1/PD-1 BM immune profile, suggesting that SMM patients could be an interesting target for PD-L1/PD-1 inhibition therapy, in light of their less compromised and more responsive immune-compartment

Spectral extension of the quantum group cotangent bundle

The structure of a cotangent bundle is investigated for quantum linear groups GLq(n) and SLq(n). Using a q-version of the Cayley-Hamilton theorem we construct an extension of the algebra of differential operators on SLq(n) (otherwise called the Heisenberg double) by spectral values of the matrix of right invariant vector fields. We consider two applications for the spectral extension. First, we describe the extended Heisenberg double in terms of a new set of generators -- the Weyl partners of the spectral variables. Calculating defining relations in terms of these generators allows us to derive SLq(n) type dynamical R-matrices in a surprisingly simple way. Second, we calculate an evolution operator for the model of q-deformed isotropic top introduced by A.Alekseev and L.Faddeev. The evolution operator is not uniquely defined and we present two possible expressions for it. The first one is a Riemann theta function in the spectral variables. The second one is an almost free motion evolution operator in terms of logarithms of the spectral variables. Relation between the two operators is given by a modular functional equation for Riemann theta function.Comment: 38 pages, no figure

Regular Conjugacy Classes in the Weyl Group and Integrable Hierarchies

Generalized KdV hierarchies associated by Drinfeld-Sokolov reduction to grade one regular semisimple elements from non-equivalent Heisenberg subalgebras of a loop algebra \G\otimes{\bf C}[\lambda,\lambda^{-1}] are studied. The graded Heisenberg subalgebras containing such elements are labelled by the regular conjugacy classes in the Weyl group {\bf W}(\G) of the simple Lie algebra \G. A representative w\in {\bf W}(\G) of a regular conjugacy class can be lifted to an inner automorphism of \G given by $\hat w=\exp\left(2i\pi {\rm ad I_0}/m\right)$, where $I_0$ is the defining vector of an $sl_2$ subalgebra of \G.The grading is then defined by the operator $d_{m,I_0}=m\lambda {d\over d\lambda} + {\rm ad} I_0$ and any grade one regular element $\Lambda$ from the Heisenberg subalgebra associated to $[w]$ takes the form $\Lambda = (C_+ +\lambda C_-)$, where $[I_0, C_-]=-(m-1) C_-$ and $C_+$ is included in an $sl_2$ subalgebra containing $I_0$. The largest eigenvalue of ${\rm ad}I_0$ is $(m-1)$ except for some cases in $F_4$, $E_{6,7,8}$. We explain how these Lie algebraic results follow from known results and apply them to construct integrable systems.If the largest ${\rm ad} I_0$ eigenvalue is $(m-1)$, then using any grade one regular element from the Heisenberg subalgebra associated to $[w]$ we can construct a KdV system possessing the standard \W-algebra defined by $I_0$ as its second Poisson bracket algebra. For \G a classical Lie algebra, we derive pseudo-differential Lax operators for those non-principal KdV systems that can be obtained as discrete reductions of KdV systems related to $gl_n$. Non-abelian Toda systems are also considered.Comment: 44 pages, ENSLAPP-L-493/94, substantial revision, SWAT-95-77. (use OLATEX (preferred) or LATEX

Digital image analysis of liver collagen predicts clinical outcome of recurrent hepatitis C virus 1 year after liver transplantation.

Clinical outcomes of recurrent hepatitis C virus after liver transplantation are difficult to predict. We evaluated collagen proportionate area (CPA), a quantitative histological index, at 1 year with respect to the first episode of clinical decompensation. Patients with biopsies at 1 year after liver transplantation were evaluated by Ishak stage/grade, and biopsy samples stained with Sirius red for digital image analysis were evaluated for CPA. Cox regression was used to evaluate variables associated with first appearance of clinical decompensation. Receiver operating characteristic (ROC) curves were also used. A total of 135 patients with median follow-up of 76 months were evaluated. At 1 year, median CPA was 4.6% (0.2%-36%) and Ishak stage was 0-2 in 101 patients, 3-4 in 23 patients, and 5-6 in 11 patients. Decompensation occurred in 26 (19.3%) at a median of 61 months (15-138). Univariately, CPA, tacrolimus monotherapy, and Ishak stage/grade at 1 year were associated with decompensation; upon multivariate analysis, only CPA was associated with decompensation (P = 0.010; Exp(B) = 1.169; 95%CI, 1.037-1.317). Area under the ROC curve was 0.97 (95%CI, 0.94-0.99). A cutoff value of 6% of CPA had 82% sensitivity and 95% specificity for decompensation. In the 89 patients with hepatic venous pressure gradient (HVPG) measurement, similar results were obtained. When both cutoffs of CPA > 6% and HVPG >= 6 mm Hg were used, all patients decompensated. Thus, CPA at 1-year biopsy after liver transplantation was highly predictive of clinical outcome in patients infected with hepatitis C virus who underwent transplantation, better than Ishak stage or HVPG. Liver Transpl 17:178-188, 2011. (C) 2011 AASLD