A six-parameter space to describe galaxy diversification

Galaxy diversification proceeds by transforming events like accretion, interaction or mergers. These explain the formation and evolution of galaxies that can now be described with many observables. Multivariate analyses are the obvious tools to tackle the datasets and understand the differences between different kinds of objects. However, depending on the method used, redundancies, incompatibilities or subjective choices of the parameters can void the usefulness of such analyses. The behaviour of the available parameters should be analysed before an objective reduction of dimensionality and subsequent clustering analyses can be undertaken, especially in an evolutionary context. We study a sample of 424 early-type galaxies described by 25 parameters, ten of which are Lick indices, to identify the most structuring parameters and determine an evolutionary classification of these objects. Four independent statistical methods are used to investigate the discriminant properties of the observables and the partitioning of the 424 galaxies: Principal Component Analysis, K-means cluster analysis, Minimum Contradiction Analysis and Cladistics. (abridged)Comment: Accepted for publicationin A\&

Pseudorandom Generators for Width-3 Branching Programs

We construct pseudorandom generators of seed length $\tilde{O}(\log(n)\cdot \log(1/\epsilon))$ that $\epsilon$-fool ordered read-once branching programs (ROBPs) of width $3$ and length $n$. For unordered ROBPs, we construct pseudorandom generators with seed length $\tilde{O}(\log(n) \cdot \mathrm{poly}(1/\epsilon))$. This is the first improvement for pseudorandom generators fooling width $3$ ROBPs since the work of Nisan [Combinatorica, 1992]. Our constructions are based on the `iterated milder restrictions' approach of Gopalan et al. [FOCS, 2012] (which further extends the Ajtai-Wigderson framework [FOCS, 1985]), combined with the INW-generator [STOC, 1994] at the last step (as analyzed by Braverman et al. [SICOMP, 2014]). For the unordered case, we combine iterated milder restrictions with the generator of Chattopadhyay et al. [CCC, 2018]. Two conceptual ideas that play an important role in our analysis are: (1) A relabeling technique allowing us to analyze a relabeled version of the given branching program, which turns out to be much easier. (2) Treating the number of colliding layers in a branching program as a progress measure and showing that it reduces significantly under pseudorandom restrictions. In addition, we achieve nearly optimal seed-length $\tilde{O}(\log(n/\epsilon))$ for the classes of: (1) read-once polynomials on $n$ variables, (2) locally-monotone ROBPs of length $n$ and width $3$ (generalizing read-once CNFs and DNFs), and (3) constant-width ROBPs of length $n$ having a layer of width $2$ in every consecutive $\mathrm{poly}\log(n)$ layers.Comment: 51 page

The Power of Super-logarithmic Number of Players

In the `Number-on-Forehead\u27 (NOF) model of multiparty communication, the input is a k times m boolean matrix A (where k is the number of players) and Player i sees all bits except those in the i-th row, and the players communicate by broadcast in order to evaluate a specified function f at A. We discover new computational power when k exceeds log m. We give a protocol with communication cost poly-logarithmic in m, for block composed functions with limited block width. These are functions of the form f o g where f is a symmetric b-variate function, and g is a (kr)-variate function and (f o g)(A) is defined, for a k times (br) matrix to be f(g(A-1),...,g(A-b)) where A-i is the i-th (k times r) block of A. Our protocol works provided that k > 1+ ln b + (2 to the power of r). Ada et al. (ICALP\u272012) previously obtained simultaneous and deterministic efficient protocols for composed functions of block-width one. The new protocol is the first to work for block composed functions with block-width greather than one. Moreover, it is simultaneous, with vanishingly small error probability, if public coin randomness is allowed. The deterministic and zero-error version barely uses interaction

Two-Source Dispersers for Polylogarithmic Entropy and Improved Ramsey Graphs

In his 1947 paper that inaugurated the probabilistic method, Erd\H{o}s proved the existence of $2\log{n}$-Ramsey graphs on $n$ vertices. Matching Erd\H{o}s' result with a constructive proof is a central problem in combinatorics, that has gained a significant attention in the literature. The state of the art result was obtained in the celebrated paper by Barak, Rao, Shaltiel and Wigderson [Ann. Math'12], who constructed a $2^{2^{(\log\log{n})^{1-\alpha}}}$-Ramsey graph, for some small universal constant $\alpha > 0$. In this work, we significantly improve the result of Barak~\etal and construct $2^{(\log\log{n})^c}$-Ramsey graphs, for some universal constant $c$. In the language of theoretical computer science, our work resolves the problem of explicitly constructing two-source dispersers for polylogarithmic entropy

Equation of State in Numerical Relativistic Hydrodynamics

Relativistic temperature of gas raises the issue of the equation of state (EoS) in relativistic hydrodynamics. We study the EoS for numerical relativistic hydrodynamics, and propose a new EoS that is simple and yet approximates very closely the EoS of the single-component perfect gas in relativistic regime. We also discuss the calculation of primitive variables from conservative ones for the EoS's considered in the paper, and present the eigenstructure of relativistic hydrodynamics for a general EoS, in a way that they can be used to build numerical codes. Tests with a code based on the Total Variation Diminishing (TVD) scheme are presented to highlight the differences induced by different EoS's.Comment: To appear in the ApJS September 2006, v166n1 issue. Pdf with full resolution figures can be downloaded from http://canopus.cnu.ac.kr/ryu/ryuetal.pd

Promoting and Empowering the RF and Microwave Community in Costa Rica

This article describes a recent and very fruitful IEEE MTT-S initiative in Latin America focusing on Costa Rica. Envisaged by the Membership and Geographical Activities (MGA) Committee of the MTT-S Administrative Committee (AdCom), this initiative, which was implemented by the end of 2022, aimed at developing MTT-S membership, volunteer base, and increased engagement in MTT-S activities in Region 9 of IEEE, especially focusing on Costa Rica. The delegation consisting of the MTT-S MGA Chair, Goutam Chattopadhyay, and the MTT-S Region 9 Coordinator, José Rayas-Sánchez, visited San Jose, Costa Rica. The 2022 MTT-S President, Rashaunda Henderson, was to accompany the delegation but had to drop out at the last moment due to some unavoidable circumstances. The delegation carried MTT-S President’s message to the microwave community in Costa Rica. This article presents the rationale and goals of the MTT-S delegation, the planning for the initiative, the agenda and activities, and the outcomes achieved. Several months after its implementation, the results obtained indicate that the initiative was very successful, confirming it as an effective strategy to promote RF and microwave-related technical activities and revitalize communities in similar emerging regions of the world.ITESO, A.C

Analysis of Smart Composite Structures Including Debonding

Smart composite structures with distributed sensors and actuators have the capability to actively respond to a changing environment while offering significant weight savings and additional passive controllability through ply tailoring. Piezoelectric sensing and actuation of composite laminates is the most promising concept due to the static and dynamic control capabilities. Essential to the implementation of these smart composites are the development of accurate and efficient modeling techniques and experimental validation. This research addresses each of these important topics. A refined higher order theory is developed to model composite structures with surface bonded or embedded piezoelectric transducers. These transducers are used as both sensors and actuators for closed loop control. The theory accurately captures the transverse shear deformation through the thickness of the smart composite laminate while satisfying stress free boundary conditions on the free surfaces. The theory is extended to include the effect of debonding at the actuator-laminate interface. The developed analytical model is implemented using the finite element method utilizing an induced strain approach for computational efficiency. This allows general laminate geometries and boundary conditions to be analyzed. The state space control equations are developed to allow flexibility in the design of the control system. Circuit concepts are also discussed. Static and dynamic results of smart composite structures, obtained using the higher order theory, are correlated with available analytical data. Comparisons, including debonded laminates, are also made with a general purpose finite element code and available experimental data. Overall, very good agreement is observed. Convergence of the finite element implementation of the higher order theory is shown with exact solutions. Additional results demonstrate the utility of the developed theory to study piezoelectric actuation of composite laminates with pre-existing debonding. Significant changes in the modes shapes and reductions in the control authority result due to partially debonded actuators. An experimental investigation addresses practical issues, such as circuit design and implementation, associated with piezoelectric sensing and actuation of composite laminates. Composite specimens with piezoelectric transducers were designed, constructed and tested to validate the higher order theory. These specimens were tested with various stacking sequences, debonding lengths and gains for both open and closed loop cases. Frequency changes of 15% and damping on the order of more than 20% of critical damping, via closed loop control, was achieved. Correlation with the higher order theory is very good. Debonding is shown to adversely affect the open and closed loop frequencies, damping ratios, settling time and control authority

Double-Exchange Model on Triangle Chain

We study ground state properties of the double-exchange model on triangle chain in the classical limit on $t_{2g}$ spins. The ground state is determined by a competition among the kinetic energy of the $e_g$ electron, the antiferromagnetic exchange energy between the $t_{2g}$ spins, and frustration due to a geometric structure of the lattice. The phase diagrams are obtained numerically for two kinds of the models which differ only in the transfer integral being real or complex. The properties of the states are understood from the viewpoint of the spin-induced Peierls instability. The results suggest the existence of a chiral glass phase which is characterized by a local spin chirality and a continuous degeneracy.Comment: 6 pages, 4 figure

The Non-local Kardar-Parisi-Zhang Equation With Spatially Correlated Noise

The effects of spatially correlated noise on a phenomenological equation equivalent to a non-local version of the Kardar-Parisi-Zhang equation are studied via the dynamic renormalization group (DRG) techniques. The correlated noise coupled with the long ranged nature of interactions prove the existence of different phases in different regimes, giving rise to a range of roughness exponents defined by their corresponding critical dimensions. Finally self-consistent mode analysis is employed to compare the non-KPZ exponents obtained as a result of the long range -long range interactions with the DRG results.Comment: Plain Latex, 10 pages, 2 figures in one ps fil

Numerical optimization of integrating cavities for diffraction-limited millimeter-wave bolometer arrays

Far-infrared to millimeter-wave bolometers designed to make astronomical observations are typically encased in integrating cavities at the termination of feedhorns or Winston cones. This photometer combination maximizes absorption of radiation, enables the absorber area to be minimized, and controls the directivity of absorption, thereby reducing susceptibility to stray light. In the next decade, arrays of hundreds of silicon nitride micromesh bolometers with planar architectures will be used in ground-based, suborbital, and orbital platforms for astronomy. The optimization of integrating cavity designs is required for achieving the highest possible sensitivity for these arrays. We report numerical simulations of the electromagnetic fields in integrating cavities with an infinite plane-parallel geometry formed by a solid reflecting backshort and the back surface of a feedhorn array block. Performance of this architecture for the bolometer array camera (Bolocam) for cosmology at a frequency of 214 GHz is investigated. We explore the sensitivity of absorption efficiency to absorber impedance and backshort location and the magnitude of leakage from cavities. The simulations are compared with experimental data from a room-temperature scale model and with the performance of Bolocam at a temperature of 300 mK. The main results of the simulations for Bolocam-type cavities are that (1) monochromatic absorptions as high as 95% are achievable with <1% cross talk between neighboring cavities, (2) the optimum absorber impedances are 400 Ω/sq, but with a broad maximum from ~150 to ~700 Ω/sq, and (3) maximum absorption is achieved with absorber diameters ≥1.5λ. Good general agreement between the simulations and the experiments was found