The covert set-cover problem with application to Network Discovery

We address a version of the set-cover problem where we do not know the sets initially (and hence referred to as covert) but we can query an element to find out which sets contain this element as well as query a set to know the elements. We want to find a small set-cover using a minimal number of such queries. We present a Monte Carlo randomized algorithm that approximates an optimal set-cover of size $OPT$ within $O(\log N)$ factor with high probability using $O(OPT \cdot \log^2 N)$ queries where $N$ is the input size. We apply this technique to the network discovery problem that involves certifying all the edges and non-edges of an unknown $n$-vertices graph based on layered-graph queries from a minimal number of vertices. By reducing it to the covert set-cover problem we present an $O(\log^2 n)$-competitive Monte Carlo randomized algorithm for the covert version of network discovery problem. The previously best known algorithm has a competitive ratio of $\Omega (\sqrt{n\log n})$ and therefore our result achieves an exponential improvement

QCD ANALYSIS OF FLAVOR-NONCHANGING HADRONIC WEAK PROCESSES THROUGH NEXT-TO-LEADING ORDER

Studies in quantum chromodynamics (QCD), the fundamental theory of the strong interactions, of low-energy hadronic weak processes utilize an effective Hamiltonian framework. Below the weak-mass scale, an effective Hamiltonian contains a series of Wilson coefficients and four-quark operators that come from the operator product expansion in the Standard Model. The effective hadronic Hamiltonian pertinent to a weak process is then obtained via a renormalization group analysis in QCD from the weak-mass scale to the low-energy scale of O(2 GeV). In this thesis, the construction and phenomenological implications of such an effective Hamiltonian for flavor-conserving, parity-violating quark processes in the Standard Model will be presented. Extensive studies of QCD corrections in flavor-changing meson decays have been conducted starting already in the 1990s. But the status in the flavor-conserving sector is completely different, and such rigorous studies have been lacking. In this work, we establish a robust connection between flavor-conserving and flavor-changing physics and utilize it to find the relevant anomalous dimension matrices for flavor-nonchanging processes through next-to-leading order in QCD. The anomalous dimension matrices represent the renormalization and mixing profile of the operators in the presence of QCD corrections and are an essential ingredient in the renormalization group flow between energy scales. Following the computation of the complete effective low-energy Hamiltonian at GeV scales, we are able to apply it to the study of hadronic parity-violating processes and compute its quantifying parameters, the parity-breaking meson nucleon couplings. The thus computed couplings are shown to be in good agreement with their extracted values from phenomenological analyses of recent, precise measurements of the parity-violating asymmetry in neutron-spin reversal in few-body low-energy nuclear reactions. This has been accomplished for the first time. Finally, we are also able to discuss how this effective Hamiltonian can be applied to studies of weak effects in the hadronic decays of flavor-neutral mesons, such as, η, η′, resulting in P and CP violation. We note how future experiments and lattice QCD studies could sharpen our findings and that our study serves as an essential guide for these future endeavors in arriving at a robust description of hadronic parity violations

Low Power Reversible Parallel Binary Adder/Subtractor

In recent years, Reversible Logic is becoming more and more prominent technology having its applications in Low Power CMOS, Quantum Computing, Nanotechnology, and Optical Computing. Reversibility plays an important role when energy efficient computations are considered. In this paper, Reversible eight-bit Parallel Binary Adder/Subtractor with Design I, Design II and Design III are proposed. In all the three design approaches, the full Adder and Subtractors are realized in a single unit as compared to only full Subtractor in the existing design. The performance analysis is verified using number reversible gates, Garbage input/outputs and Quantum Cost. It is observed that Reversible eight-bit Parallel Binary Adder/Subtractor with Design III is efficient compared to Design I, Design II and existing design.Comment: 12 pages,VLSICS Journa

Towards a unified treatment of ΔS=0\Delta S=0 parity violation in low-energy nuclear processes

We revisit the unified treatment of low-energy hadronic parity violation espoused by Desplanques, Donoghue, and Holstein to the end of an ab initio treatment of parity violation in low-energy nuclear processes within the Standard Model. We use our improved effective Hamiltonian and precise non-perturbative assessments of the quark charges of the nucleon within lattice QCD to make new assessments of the parity-violating meson-nucleon coupling constants. Comparing with recent, precise measurements of hadronic parity violation in few-body nuclear reactions, we find improved agreement with these experimental results, though some tensions remain. We thus note the broader problem of comparing low-energy constants from nuclear and few-nucleon systems, considering, too, unresolved theoretical issues in connecting an ab initio, effective Hamiltonian approach to chiral effective theories. We note how future experiments could sharpen the emerging picture, promoting the study of hadronic parity violation as a laboratory for testing ``end-to-end'' theoretical descriptions of weak processes in hadrons and nuclei at low energies.Comment: 13 pages, REVTeX, 1 figure; note partial overlap in content with arXiv:2203.00033v1 (not v2

Constraining the average magnetic field in galaxy clusters with current and upcoming CMB surveys

Galaxy clusters that host radio halos indicate the presence of population(s) of non-thermal electrons. These electrons can scatter low-energy photons of the Cosmic Microwave Background, resulting in the non-thermal Sunyaev-Zeldovich (ntSZ) effect. We measure the average ntSZ signal from 62 radio-halo hosting clusters using the $Planck$ multi-frequency all-sky maps. We find no direct evidence of the ntSZ signal in the $Planck$ data. Combining the upper limits on the non-thermal electron density with the average measured synchrotron power collected from the literature, we place lower limits on the average magnetic field strength in our sample. The lower limit on the volume-averaged magnetic field is $0.1-0.01\,\mu$G, depending on the assumed power-law distribution of electron energies. We further explore the potential improvement of these constraints from the upcoming Simons Observatory and Fred Young Submillimeter Telescope (FYST) of the CCAT-prime collaboration. We find that combining these two experiments, the constraints will improve by a factor of $3-4$, which can be sufficient to rule out some power-law models.Comment: 25 pages, 7 figures. Submitted to JCA

Centralized Admission: A Novel Student-Centric E-Governance Process

e-governance initiative has helped many governmental organizations to carry out their services transparently, efficiently, and democratically. The admission process in many of the universities in Karnataka is usually manual. The process suffers from redundancy of data and workforce and the process itself is expensive. For the first time in any University in Karnataka, in 2009, an automated system for Post Graduate admissions was designed, developed and implemented for Bangalore University. This e-governance admission system has been in use in the University for the last four years. The process was started as a skeleton model and more services were added later in subsequent academic years during admission. It was found that the system was foolproof. It transformed the whole admission process into a single-window system. Admission Approval, Fee Payment, Hostel Admissions, and Issue of Library Cards were thus brought under a single-window system. This paper compares the novel e-governance initiative with that of the pervious system of admission. It also compares the Bangalore University model with other automated admission models in Karnataka. It investigates the performance of the e-governance initiative in reducing workforce and redundancy. It records the find that the e-governance process has helped the University and its stakeholders in rendering the admission system transparent. Many other Universities in Karnataka are now following this model for their admission

A result on the distribution of quadratic residues with applications to elliptic curve cryptography

In this paper, we prove that for any polynomial function f of fixed degree without multiple roots, the probability that all the (f(x + 1), f(x + 2), ..., f(x +κ)) are quadratic non-residue is ≈ 1/2κ. In particular for f(x) = x3 + ax + b corresponding to the elliptic curve y2 = x3 + ax + b, it implies that the quadratic residues (f(x + 1), f(x + 2), . . . in a finite field are sufficiently randomly distributed. Using this result we describe an efficient implementation of El-Gamal Cryptosystem. that requires efficient computation of a mapping between plain-texts and the points on the elliptic curve