sl(N) Onsager's Algebra and Integrability

We define an $sl(N)$ analog of Onsager's Algebra through a finite set of relations that generalize the Dolan Grady defining relations for the original Onsager's Algebra. This infinite-dimensional Lie Algebra is shown to be isomorphic to a fixed point subalgebra of $sl(N)$ Loop Algebra with respect to a certain involution. As the consequence of the generalized Dolan Grady relations a Hamiltonian linear in the generators of $sl(N)$ Onsager's Algebra is shown to posses an infinite number of mutually commuting integrals of motion

Observation of discrete time-crystalline order in a disordered dipolar many-body system

Understanding quantum dynamics away from equilibrium is an outstanding challenge in the modern physical sciences. It is well known that out-of-equilibrium systems can display a rich array of phenomena, ranging from self-organized synchronization to dynamical phase transitions. More recently, advances in the controlled manipulation of isolated many-body systems have enabled detailed studies of non-equilibrium phases in strongly interacting quantum matter. As a particularly striking example, the interplay of periodic driving, disorder, and strong interactions has recently been predicted to result in exotic "time-crystalline" phases, which spontaneously break the discrete time-translation symmetry of the underlying drive. Here, we report the experimental observation of such discrete time-crystalline order in a driven, disordered ensemble of $\sim 10^6$ dipolar spin impurities in diamond at room-temperature. We observe long-lived temporal correlations at integer multiples of the fundamental driving period, experimentally identify the phase boundary and find that the temporal order is protected by strong interactions; this order is remarkably stable against perturbations, even in the presence of slow thermalization. Our work opens the door to exploring dynamical phases of matter and controlling interacting, disordered many-body systems.Comment: 6 + 3 pages, 4 figure

The Chiral Potts Models Revisited

In honor of Onsager's ninetieth birthday, we like to review some exact results obtained so far in the chiral Potts models and to translate these results into language more transparent to physicists, so that experts in Monte Carlo calculations, high and low temperature expansions, and various other methods, can use them. We shall pay special attention to the interfacial tension $\epsilon_r$ between the $k$ state and the $k-r$ state. By examining the ground states, it is seen that the integrable line ends at a superwetting point, on which the relation $\epsilon_r=r\epsilon_1$ is satisfied, so that it is energetically neutral to have one interface or more. We present also some partial results on the meaning of the integrable line for low temperatures where it lives in the non-wet regime. We make Baxter's exact results more explicit for the symmetric case. By performing a Bethe Ansatz calculation with open boundary conditions we confirm a dilogarithm identity for the low-temperature expansion which may be new. We propose a new model for numerical studies. This model has only two variables and exhibits commensurate and incommensurate phase transitions and wetting transitions near zero temperature. It appears to be not integrable, except at one point, and at each temperature there is a point, where it is almost identical with the integrable chiral Potts model.Comment: J. Stat. Phys., LaTeX using psbox.tex and AMS fonts, 69 pages, 30 figure

Gemcitabine and docetaxel as first-line treatment for advanced urothelial carcinoma: a phase II study

The purpose of the study was to investigate the toxicity and efficacy of the combination of gemcitabine and docetaxel in untreated advanced urothelial carcinoma. Patients with previously untreated, locally advanced/recurrent or metastatic urothelial carcinoma stage-IV disease were eligible. Patients with Performance status: PS ECOG >3 or age >75 years or creatinine clearance <50 ml min−1 were excluded. Study treatment consisted of docetaxel 75 mg m−2 (day 8) and gemcitabine 1000 mg m−2 (days 1+8), every 21 days for a total of six to nine cycles. A total of 31 patients with urothelial bladder cancer, 25 men and six women, aged 42–74 (median 64) years were enrolled. The majority of patients had a good PS (51.6%; PS 0). In all, 15 (48.3%) patients had locally advanced or recurrent disease only and 16 (54.8%) presented with distant metastatic spread, with multiple site involvement in 22.5%. Toxicity was primarily haematologic, and the most frequent grade 3–4 toxicities were anaemia 11 (6.7%) thrombocytopenia eight (4.9%), and neutropenia 45 (27.6%), with 10 (6.1%) episodes of febrile neutropenia. No toxic deaths occurred. A number of patients had some cardiovascular morbidity (38.7%). Nonhaematological toxicities except alopecia (29 patients) were mild. Overall response rate was 51.6%, including four complete responses (12.9%) and 12 partial responses (38.7%), while a further five patients had disease stabilisation (s.d. 16.1%). The median time to progression was 8 months (95% CI 5.1–9.2 months) and the median overall survival was 15 months (95% CI 11.2–18.5 months), with 1-year survival rate of 60%. In conclusion, this schedule of gemcitabine and docetaxel is very active and well tolerated as a first-line treatment for advanced/relapsing or metastatic urothelial carcinoma. Although its relative efficacy and tolerance as compared to classic MVAC should be assessed in a phase III setting, the favourable toxicity profile of this regimen may offer an interesting alternative, particularly in patients with compromised renal function or cardiovascular disease

Multifrequency Strategies for the Identification of Gamma-Ray Sources

More than half the sources in the Third EGRET (3EG) catalog have no firmly established counterparts at other wavelengths and are unidentified. Some of these unidentified sources have remained a mystery since the first surveys of the gamma-ray sky with the COS-B satellite. The unidentified sources generally have large error circles, and finding counterparts has often been a challenging job. A multiwavelength approach, using X-ray, optical, and radio data, is often needed to understand the nature of these sources. This chapter reviews the technique of identification of EGRET sources using multiwavelength studies of the gamma-ray fields.Comment: 35 pages, 22 figures. Chapter prepared for the book "Cosmic Gamma-ray Sources", edited by K.S. Cheng and G.E. Romero, to be published by Kluwer Academic Press, 2004. For complete article and higher resolution figures, go to: http://www.astro.columbia.edu/~muk/mukherjee_multiwave.pd

Linear, Deterministic, and Order-Invariant Initialization Methods for the K-Means Clustering Algorithm

Over the past five decades, k-means has become the clustering algorithm of choice in many application domains primarily due to its simplicity, time/space efficiency, and invariance to the ordering of the data points. Unfortunately, the algorithm's sensitivity to the initial selection of the cluster centers remains to be its most serious drawback. Numerous initialization methods have been proposed to address this drawback. Many of these methods, however, have time complexity superlinear in the number of data points, which makes them impractical for large data sets. On the other hand, linear methods are often random and/or sensitive to the ordering of the data points. These methods are generally unreliable in that the quality of their results is unpredictable. Therefore, it is common practice to perform multiple runs of such methods and take the output of the run that produces the best results. Such a practice, however, greatly increases the computational requirements of the otherwise highly efficient k-means algorithm. In this chapter, we investigate the empirical performance of six linear, deterministic (non-random), and order-invariant k-means initialization methods on a large and diverse collection of data sets from the UCI Machine Learning Repository. The results demonstrate that two relatively unknown hierarchical initialization methods due to Su and Dy outperform the remaining four methods with respect to two objective effectiveness criteria. In addition, a recent method due to Erisoglu et al. performs surprisingly poorly.Comment: 21 pages, 2 figures, 5 tables, Partitional Clustering Algorithms (Springer, 2014). arXiv admin note: substantial text overlap with arXiv:1304.7465, arXiv:1209.196

Phase II multicentre study of docetaxel plus cisplatin in patients with advanced urothelial cancer

A multicentre phase II trial was undertaken to evaluate the activity and toxicity of docetaxel plus cisplatin as first-line chemotherapy in patients with urothelial cancer. Thirty-eight patients with locally advanced or metastatic transitional-cell carcinoma of the bladder, renal pelvis or ureter received the combination of docetaxel 75 mg m−2 and cisplatin 75 mg m−2 on day 1 and repeated every 21 days, to a maximum of six cycles. The median delivered dose-intensity was 98% (range 79–102%) of the planned dose for both drugs. There were seven complete responses and 15 partial responses, for and overall response rate of 58% (95% CI, 41–74%). Responses were even seen in three patients with hepatic metastases. The median time to progression was 6.9 months, and the median overall survival was 10.4 months. Two patients who achieved CR status remain free of disease at 4 and 3 years respectively. Grade 3–4 granulocytopenia occurred in 27 patients, resulting in five episodes of febrile neutropenia. There was one toxic death in a patient with grade 4 granulocytopenia who developed acute abdomen. Grade 3–4 thrombocytopenia was rare (one patient). Other grade 3–4 toxicities observed were anaemia (three patients), vomiting (five patients), diarrhoea (four patients), peripheral neuropathy (two patients) and non-neutropenic infections (seven patients). Docetaxel plus cisplatin is an effective and well-tolerated regimen for the treatment of advanced urothelial cancer, and warrants further investigation

Gene duplication and fragmentation in the zebra finch major histocompatibility complex

BACKGROUND: Due to its high polymorphism and importance for disease resistance, the major histocompatibility complex (MHC) has been an important focus of many vertebrate genome projects. Avian MHC organization is of particular interest because the chicken Gallus gallus, the avian species with the best characterized MHC, possesses a highly streamlined minimal essential MHC, which is linked to resistance against specific pathogens. It remains unclear the extent to which this organization describes the situation in other birds and whether it represents a derived or ancestral condition. The sequencing of the zebra finch Taeniopygia guttata genome, in combination with targeted bacterial artificial chromosome (BAC) sequencing, has allowed us to characterize an MHC from a highly divergent and diverse avian lineage, the passerines. RESULTS: The zebra finch MHC exhibits a complex structure and history involving gene duplication and fragmentation. The zebra finch MHC includes multiple Class I and Class II genes, some of which appear to be pseudogenes, and spans a much more extensive genomic region than the chicken MHC, as evidenced by the presence of MHC genes on each of seven BACs spanning 739 kb. Cytogenetic (FISH) evidence and the genome assembly itself place core MHC genes on as many as four chromosomes with TAP and Class I genes mapping to different chromosomes. MHC Class II regions are further characterized by high endogenous retroviral content. Lastly, we find strong evidence of selection acting on sites within passerine MHC Class I and Class II genes. CONCLUSION: The zebra finch MHC differs markedly from that of the chicken, the only other bird species with a complete genome sequence. The apparent lack of synteny between TAP and the expressed MHC Class I locus is in fact reminiscent of a pattern seen in some mammalian lineages and may represent convergent evolution. Our analyses of the zebra finch MHC suggest a complex history involving chromosomal fission, gene duplication and translocation in the history of the MHC in birds, and highlight striking differences in MHC structure and organization among avian lineages