A new (in)finite dimensional algebra for quantum integrable models

A new (in)finite dimensional algebra which is a fundamental dynamical symmetry of a large class of (continuum or lattice) quantum integrable models is introduced and studied in details. Finite dimensional representations are constructed and mutually commuting quantities - which ensure the integrability of the system - are written in terms of the fundamental generators of the new algebra. Relation with the deformed Dolan-Grady integrable structure recently discovered by one of the authors and Terwilliger's tridiagonal algebras is described. Remarkably, this (in)finite dimensional algebra is a ``$q-$deformed'' analogue of the original Onsager's algebra arising in the planar Ising model. Consequently, it provides a new and alternative algebraic framework for studying massive, as well as conformal, quantum integrable models.Comment: 17 pages; LaTeX file with amssymb; v2: typos corrected, references added, minor changes;v3: other typos corrected, version to appear in Nucl.Phys.

A deformed analogue of Onsager's symmetry in the XXZ open spin chain

The XXZ open spin chain with general integrable boundary conditions is shown to possess a q-deformed analogue of the Onsager's algebra as fundamental non-abelian symmetry which ensures the integrability of the model. This symmetry implies the existence of a finite set of independent mutually commuting nonlocal operators which form an abelian subalgebra. The transfer matrix and local conserved quantities, for instance the Hamiltonian, are expressed in terms of these nonlocal operators. It follows that Onsager's original approach of the planar Ising model can be extended to the XXZ open spin chain.Comment: 12 pages; LaTeX file with amssymb; v2: typos corrected, clarifications in the text; v3: minor changes in references, version to appear in JSTA

A Proteomic Approach for the Diagnosis of ‘Oketsu’ (blood stasis), a Pathophysiologic Concept of Japanese Traditional (Kampo) Medicine

‘Oketsu’ is a pathophysiologic concept in Japanese traditional (Kampo) medicine, primarily denoting blood stasis/stagnant syndrome. Here we have explored plasma protein biomarkers and/or diagnostic algorithms for ‘Oketsu’. Sixteen rheumatoid arthritis (RA) patients were treated with keishibukuryogan (KBG), a representative Kampo medicine for improving ‘Oketsu’. Plasma samples were diagnosed as either having an ‘Oketsu’ (n = 19) or ‘non-Oketsu’ (n = 29) state according to Terasawa's ‘Oketsu’ scoring system. Protein profiles were obtained by surface-enhanced laser desorption/ionization time-of-flight mass spectrometry (SELDI-TOF MS) and hierarchical clustering and decision tree analyses were performed. KBG treatment for 4 or 12 weeks decreased the ‘Oketsu’ scores significantly. SELDI protein profiles gave 266 protein peaks, whose expression was significantly different between the ‘Oketsu’ and ‘non-Oketsu’ states. Hierarchical clustering gave three major clusters (I, II, III). The majority (68.4%) of ‘Oketsu’ samples were clustered into one cluster as the principal component of cluster I. The remaining ‘Oketsu’ profiles constituted a minor component of cluster II and were all derived from patients cured of the ‘Oketsu’ state at 12 weeks. Construction of the decision tree addressed the possibility of developing a diagnostic algorithm for ‘Oketsu’. A reduction in measurement/pre-processing conditions (from 55 to 16) gave a similar outcome in the clustering and decision tree analyses. The present study suggests that the pathophysiologic concept of Kampo medicine ‘Oketsu’ has a physical basis in terms of the profile of blood proteins. It may be possible to establish a set of objective criteria for diagnosing ‘Oketsu’ using a combination of proteomic and bioinformatics-based classification methods

Aberrant Calcium Signals in Reactive Astrocytes: A Key Process in Neurological Disorders

Astrocytes are abundant cells in the brain that regulate multiple aspects of neural tissue homeostasis by providing structural and metabolic support to neurons, maintaining synaptic environments and regulating blood flow. Recent evidence indicates that astrocytes also actively participate in brain functions and play a key role in brain disease by responding to neuronal activities and brain insults. Astrocytes become reactive in response to injury and inflammation, which is typically described as hypertrophy with increased expression of glial fibrillary acidic protein (GFAP). Reactive astrocytes are frequently found in many neurological disorders and are a hallmark of brain disease. Furthermore, reactive astrocytes may drive the initiation and progression of disease processes. Recent improvements in the methods to visualize the activity of reactive astrocytes in situ and in vivo have helped elucidate their functions. Ca2+ signals in reactive astrocytes are closely related to multiple aspects of disease and can be a good indicator of disease severity/state. In this review, we summarize recent findings concerning reactive astrocyte Ca2+ signals. We discuss the molecular mechanisms underlying aberrant Ca2+ signals in reactive astrocytes and the functional significance of aberrant Ca2+ signals in neurological disorders