On c‐Bhaskar Rao designs with block size 4

Several new families of c‐Bhaskar Rao designs with block size 4 are constructed. The necessary conditions for the existence of a c‐BRD (υ,4,λ) are that: (1)λ_min=?λ/3 ≤ c ≤ λ and (2a) c≡λ (mod 2), if υ > 4 or (2b) c≡ λ (mod 4), if υ = 4 or (2c) c≠ λ ? 2, if υ = 5. It is proved that these conditions are necessary, and are sufficient for most pairs of c and λ; in particular, they are sufficient whenever λ?c ≠ 2 for c > 0 and whenever c ? λ_min≠ 2 for c < 0. For c < 0, the necessary conditions are sufficient for υ> 101; for the classic Bhaskar Rao designs, i.e., c = 0, we show the necessary conditions are sufficient with the possible exception of 0‐BRD (υ,4,2)'s for υ≡ 4 (mod 6). © 2002 Wiley Periodicals, Inc. J Combin Designs 10: 361–386, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jcd.10009     

A Helson-Lowdenslager-deBranges Theorem in

This paper presents a generalization of the invariant subspace theorem of Helson and Lowdenslager along the lines of de Branges' generalization of Beurling's theorem.

     

Bohr's inequality for uniform algebras

We prove a uniform algebra analogue of a classical inequality of Bohr's concerning Fourier coefficients of bounded holomorphic functions. The classical inequality follows trivially.

     

Group divisible designs with three unequal groups and larger first index

We show the necessary conditions are sufficient for the existence of group divisible designs (or PBIBDs) with block size k=3 with three groups of size (n,2,1) for any n≥2 and any two indices with λ₁>λ₂.     

Design of a Very Small Residual Dispersion Fiber System for DWDM Operation Over the Entire C - & L- Bands of EDFA

We have given design of a very small residual dispersion fiber system consisting of a small dispersion fiber(SDF) with flat modal field and a corresponding dual core coaxial dispersion compensating fiber (DCF).     

Interpretation of anomalous normal state optical conductivity of La-Sr-CuO cuprates

The observed frequency dependent optical response of hole doped cuprate La_1.85Sr_0.15CuO₄ superconductors, has been theoretically analysed. Starting from an effective two-dimensional (2D) interaction potential for superlattice of hole doped cuprates treated as a layered electron gas, the spectral function is formulated. Calculations of the optical conductivity σ(ω) have been made within the two-component scheme: one is the coherent Drude carriers responsible for superconductivity and the other is incoherent motion of carriers from one site to other leads to a pairing between Drude carriers. The approach accounts for the anomalies reported (frequency dependence of optical conductivity) in the optical measurements for the normal state. Estimating the effective mass from specific heat measurement and ε_∞ from band structure calculations for the low-energy charge density waves, the model has only one free parameter, the relaxation rate. The frequency dependent relaxation rates are expressed in terms of memory functions, and the coherent Drude carriers from the effective interaction potential lead to a sharp peak at zero frequency and a long tail at higher frequencies, i.e. in the infrared (IR) region. However, the hopping of carriers from one site to other (incoherent motion of doped carriers) yields a peak value in the optical conductivity centred at mid-IR (MIR) region. We find that both the Drude and hopping carriers in the superlattice of cuprates will contribute to the optical process of conduction in the CuO₂ planes and shows similar results on optical conductivity in the MIR as well as IR frequency regions as those revealed from experiments.     

Interventional Fairness with Indirect Knowledge of Unobserved Protected Attributes

The deployment of machine learning (ML) systems in applications with societal impact has motivated the study of fairness for marginalized groups. Often, the protected attribute is absent from the training dataset for legal reasons. However, datasets still contain proxy attributes that capture protected information and can inject unfairness in the ML model. Some deployed systems allow auditors, decision makers, or affected users to report issues or seek recourse by flagging individual samples. In this work, we examine such systems and consider a feedback-based framework where the protected attribute is unavailable and the flagged samples are indirect knowledge. The reported samples are used as guidance to identify the proxy attributes that are causally dependent on the (unknown) protected attribute. We work under the causal interventional fairness paradigm. Without requiring the underlying structural causal model a priori, we propose an approach that performs conditional independence tests on observed data to identify such proxy attributes. We theoretically prove the optimality of our algorithm, bound its complexity, and complement it with an empirical evaluation demonstrating its efficacy on various real-world and synthetic datasets.     

Demonstration of a 100 Hz repetition rate gain-saturated diode-pumped table-top soft x-ray laser

We demonstrate the operation of a gain-saturated table-top soft x-ray laser at 100?Hz repetition rate. The laser generates an average power of 0.15?mW at λ=18.9 nm, the highest laser power reported to date from a sub-20-nm wavelength compact source. Picosecond laser pulses of 1.5?μJ energy were produced at λ=18.9 nm by amplification in a Mo plasma created by tailoring the temporal intensity profile of single pump pulses with 1?J energy produced by a diode-pumped chirped pulse amplification Yb:YAG laser. Lasing was also obtained in the 13.9?nm line of Ni-like Ag. These results increase by an order of magnitude the repetition rate of plasma-based soft x-ray lasers opening the path to milliwatt average power table-top lasers at sub-20?nm wavelengths.