Gelfand-Dikii Brackets for Nonstandard Lax Equations

We generalize the construction of Gelfand-Dikii brackets to the case of nonstandard Lax equations. We also discuss the possible origin of Kac-Moody algebras present in such systems.Comment: 11 pages, Preprint no. UR1347, ER40685-79

End-to-end thiocyanato-bridged helical chain polymer and dichlorido-bridged copper(II) complexes with a hydrazone ligand: synthesis, characterisation by electron paramagnetic resonance and variable- temperature magnetic studies, and inhibitory effects on human colorectal carcinoma cells

The reactions of the tridentate hydrazone ligand, N’-[1-(pyridin-2-yl)ethylidene]acetohydrazide (HL), obtained by condensation of 2-acetylpyridine with acetic hyadrazide, with copper nitrate trihydrate in the presence of thiocyanate, or with CuCl2 produce two distinct coordination compounds, namely a one-dimensional helical coordination chain of [CuL(NCS)]n (1) units, and a doubly chlorido-bridged dinuclear complex [Cu2L2Cl2] (2) (where L=CH3C(O)=N − N=CCH3C5H4N). Single-crystal X-ray structural determination studies reveal that in complex 1, a deprotonated hydrazone ligand L- coordinates a copper(II) ion that is bridged to two neighbouring metal centres by SCN- anions, generating a one-dimensional helical coordination chain. In complex 2, two symmetry-related, adjacent copper(II) coordination entities are doubly chlorido-bridged, producing a dicopper entity with a Cu···Cu distance of 3.402 (1). The two coordination compounds have been fully characterised by elemental analysis, spectroscopic techniques including IR, UV– vis and electron paramagnetic resonance, and variable-temperature magnetic studies. The biological effects of 1 and 2 on the viability of human colorectal carcinoma cells (COLO-205 and HT-29) were evaluated using an MTT assay, and the results indicate that these complexes induce a decrease in cell-population growth of human colorectal carcinoma cells with apoptosis

Self-Progressing Robust Training

Enhancing model robustness under new and even adversarial environments is a crucial milestone toward building trustworthy machine learning systems. Current robust training methods such as adversarial training explicitly uses an "attack" (e.g., $\ell_{\infty}$-norm bounded perturbation) to generate adversarial examples during model training for improving adversarial robustness. In this paper, we take a different perspective and propose a new framework called SPROUT, self-progressing robust training. During model training, SPROUT progressively adjusts training label distribution via our proposed parametrized label smoothing technique, making training free of attack generation and more scalable. We also motivate SPROUT using a general formulation based on vicinity risk minimization, which includes many robust training methods as special cases. Compared with state-of-the-art adversarial training methods (PGD-l_inf and TRADES) under l_inf-norm bounded attacks and various invariance tests, SPROUT consistently attains superior performance and is more scalable to large neural networks. Our results shed new light on scalable, effective and attack-independent robust training methods.Comment: Accepted in AAAI202

A mixed valent heterometallic Cu-II/Na-I coordination polymer with sodium-phenyl bonds

A mixed valent heterometallic Cu/Na coordination polymer (1) is generated by the reaction of a Schiff base ligand, (6,6′-(1E,1′E)-(2-hydroxypropane-1,3-diyl)bis(azan-1-yl-1-ylidene) bis(methan-1-yl-1-ylidene)bis(2-methoxyphenol)) with copper(ii) acetate and sodium perchlorate. In addition to the presence of alcohol oxygen-sodium coordination bonds, the single crystal X-ray structure reveals that the 1D coordination polymer is stabilised by the formation of phenyl-sodium η-bonds, face-to-face π-π contacts and Cu-π interactions. This journal i

Di-μ-azido-bis­({N′-[1-(2-pyrid­yl-κN)ethyl­idene]acetohydrazidato-κ2 N′,O}dicopper(II))

The dimeric title compound, [Cu2(C9H10N3O)2(N3)2], is located on a crystallographic inversion center. The Cu atom is coordinated by a tridentate anionic hydrazone ligand and two bridging azide ligands in a distorted square-pyramidal coordination geometry. The non-bonding Cu⋯Cu distance is 3.238 (1) Å. Non-classical inter­molecular C—H⋯N hydrogen bonds link the dimers into chains along the c axis

Dichlorido{N′-[1-(2-pyridin-2-yl)ethyl­idene]acetohydrazide-κ2 N′,O}copper(II)

In the title compound, [CuCl2(C9H11N3O)], the CuII atom is in a distorted square-pyramidal CuCl2N2O coordination geometry. The tridentate acetohydrazide ligand chelates in a meridional fashion. The chloride ligand in the axial position forms a long Cu—Cl distance of 2.4892 (9) Å. In contrast, the Cu—Cl distance from the equatorial chloride ligand is much shorter [2.2110 (7) Å]. Inter­molecular N—H⋯Cl and C—H⋯Cl hydrogen bonds link the complexes into a three-dimensional network

Lindhard and RPA susceptibility computations in extended momentum space in electron doped cuprates

We present an approximation for efficient calculation of the Lindhard susceptibility $\chi^{L}(q,\omega)$ in a periodic system through the use of simple products of real space functions and the fast Fourier transform (FFT). The method is illustrated by providing $\chi^{L}(q,\omega)$ results for the electron doped cuprate Nd$_{2-x}$Ce$_{x}$CuO$_{4}$ extended over several Brillouin zones. These results are relevant for interpreting inelastic X-ray scattering spectra from cuprates.Comment: 6 pages, 6 figures, accepted in Physical Review

Classical N=2 W-superalgebras From Superpseudodifferential Operators

We study the supersymmetric Gelfand-Dickey algebras associated with the superpseudodifferential operators of positive as well as negative leading order. We show that, upon the usual constraint, these algebras contain the N=2 super Virasoro algebra as a subalgebra as long as the leading order is odd. The decompositions of the coefficient functions into N=1 primary fields are then obtained by covariantizing the superpseudodifferential operators. We discuss the problem of identifying N=2 supermultiplets and work out a couple of supermultiplets by explicit computations.Comment: 19 pages (Plain TeX), NHCU-HEP-94-1

Long-term Impact of Changing Childhood Malnutrition on Rotavirus Diarrhoea: Two Decades of Adjusted Association with Climate and Socio-Demographic Factors from Urban Bangladesh

Background There is strong association between childhood rotavirus, diarrhoea, climate factors and malnutrition. Conversely, a significant nutritional transition (reduced under-nutrition) with a concurrent increasing trend of rotavirus infection in last decade was also observed among under 5 children, especially in developing countries including Bangladesh. Considering the pathophysiology of rotavirus, there might be an interaction of this nutrition transition which plays a pivotal role in increasing rotavirus infection in addition to climate and other man-made factors in urban areas such as Dhaka, Bangladesh. Methods Relevant monthly data from 1993–2012 were extracted from the archive of the Diarrhoeal Disease Surveillance System of icddr, b and linked with data collected from the Dhaka station of the Bangladesh Meteorological Department (mean temperature, rainfall, sea level pressure and humidity). Seasonal autoregressive integrated moving average time series models were deployed to determine the association between the monthly proportion of rotavirus infection and underweight, stunting and wasting adjusting for climate, socio-demographic and sanitation factors. Finding The proportion of rotavirus cases among all causes diarrhoea increased from 20% in 1993 to 43% in 2012 (Chi squared for trend p = 0.010). In contrast, underweight, stunting and wasting decreased from 59%-29% (p \u3c 0.001); 53%-21% (p \u3c 0.001) and 32%-22% (p \u3c 0.001) respectively over the same period. Mean ambient temperature increased from 25.76°C-26.62°C (p = 0.07); mean rainfall, sea level pressure and mean humidity decreased from 234.92–111.75 mm (p = 0.5), 1008.30–1006.61 mm of hg (p = 0.02) and 76.63%-70.26% (p \u3c 0.001), respectively. In the adjusted model, a decrease in monthly proportion of underweight [coef.: -0.189 (95% CI:-0.376, -0.003)] and wasting [-0.265 (-0.455, -0.075)] were significantly and inversely associated with rotavirus infection. However, an inverse but insignificant association was observed for stunting [-0.070 (-0.249, 0.109)]. Interpretation The reduction of acute childhood malnutrition is significantly associated with increasing rotavirus diarrhoea among under-5 children. Thus mass vaccination in addition to interventions directed at man-made modifiable predictors for prevention and control is warranted