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1,182 results on '"Ghosh, Arijit"'

1. Testing vs Estimation for Index-Invariant Properties in the Huge Object Model

Author

Chakraborty, Sourav, Fischer, Eldar, Ghosh, Arijit, Levi, Amit, Mishra, Gopinath, and Sen, Sayantan

Subjects
Computer Science - Data Structures and Algorithms
Abstract

The Huge Object model of property testing [Goldreich and Ron, TheoretiCS 23] concerns properties of distributions supported on $\{0,1\}^n$, where $n$ is so large that even reading a single sampled string is unrealistic. Instead, query access is provided to the samples, and the efficiency of the algorithm is measured by the total number of queries that were made to them. Index-invariant properties under this model were defined in [Chakraborty et al., COLT 23], as a compromise between enduring the full intricacies of string testing when considering unconstrained properties, and giving up completely on the string structure when considering label-invariant properties. Index-invariant properties are those that are invariant through a consistent reordering of the bits of the involved strings. Here we provide an adaptation of Szemer\'edi's regularity method for this setting, and in particular show that if an index-invariant property admits an $\epsilon$-test with a number of queries depending only on the proximity parameter $\epsilon$, then it also admits a distance estimation algorithm whose number of queries depends only on the approximation parameter., Comment: 57 Pages

Published
2024

2. Testing Credibility of Public and Private Surveys through the Lens of Regression

Author

Basu, Debabrota, Chakraborty, Sourav, Chanda, Debarshi, Das, Buddha Dev, Ghosh, Arijit, and Ray, Arnab

Subjects
Computer Science - Machine Learning, Computer Science - Cryptography and Security, Statistics - Methodology, Statistics - Machine Learning
Abstract

Testing whether a sample survey is a credible representation of the population is an important question to ensure the validity of any downstream research. While this problem, in general, does not have an efficient solution, one might take a task-based approach and aim to understand whether a certain data analysis tool, like linear regression, would yield similar answers both on the population and the sample survey. In this paper, we design an algorithm to test the credibility of a sample survey in terms of linear regression. In other words, we design an algorithm that can certify if a sample survey is good enough to guarantee the correctness of data analysis done using linear regression tools. Nowadays, one is naturally concerned about data privacy in surveys. Thus, we further test the credibility of surveys published in a differentially private manner. Specifically, we focus on Local Differential Privacy (LDP), which is a standard technique to ensure privacy in surveys where the survey participants might not trust the aggregator. We extend our algorithm to work even when the data analysis has been done using surveys with LDP. In the process, we also propose an algorithm that learns with high probability the guarantees a linear regression model on a survey published with LDP. Our algorithm also serves as a mechanism to learn linear regression models from data corrupted with noise coming from any subexponential distribution. We prove that it achieves the optimal estimation error bound for $\ell_1$ linear regression, which might be of broader interest. We prove the theoretical correctness of our algorithms while trying to reduce the sample complexity for both public and private surveys. We also numerically demonstrate the performance of our algorithms on real and synthetic datasets.

Published
2024

3. About almost covering subsets of the hypercube

Author

Ghosh, Arijit, Kayal, Chandrima, and Nandi, Soumi

Subjects
Mathematics - Combinatorics, Computer Science - Discrete Mathematics, 05D40, 51D20, F.2.2, G.2.1
Abstract

Let $\mathbb{F}$ be a field, and consider the hypercube $\{ 0, 1 \}^{n}$ in $\mathbb{F}^{n}$. Sziklai and Weiner (Journal of Combinatorial Theory, Series A 2022) showed that if a polynomial $P ( X_{1}, \dots, X_{n} ) \in \mathbb{F}[ X_{1}, \dots, X_{n}]$ vanishes on every point of the hypercube $\{0,1\}^{n}$ except those with at most $r$ many ones then the degree of the polynomial will be at least $n-r$. This is a generalization of Alon and F\"uredi's fundamental result (European Journal of Combinatorics 1993) about polynomials vanishing on every point of the hypercube except at the origin (point with all zero coordinates). Sziklai and Weiner proved their interesting result using M\"{o}bius inversion formula and the Zeilberger method for proving binomial equalities. In this short note, we show that a stronger version of Sziklai and Weiner's result can be derived directly from Alon and F\"{u}redi's result., Comment: 2 pages. Fixed a typo in the proof of Theorem 4. Results unchanged

Published
2024

4. On Fourier analysis of sparse Boolean functions over certain Abelian groups

Author

Chakraborty, Sourav, Datta, Swarnalipa, Dutta, Pranjal, Ghosh, Arijit, and Sanyal, Swagato

Subjects
Computer Science - Computational Complexity
Abstract

Given an Abelian group G, a Boolean-valued function f: G -> {-1,+1}, is said to be s-sparse, if it has at most s-many non-zero Fourier coefficients over the domain G. In a seminal paper, Gopalan et al. proved "Granularity" for Fourier coefficients of Boolean valued functions over Z_2^n, that have found many diverse applications in theoretical computer science and combinatorics. They also studied structural results for Boolean functions over Z_2^n which are approximately Fourier-sparse. In this work, we obtain structural results for approximately Fourier-sparse Boolean valued functions over Abelian groups G of the form,G:= Z_{p_1}^{n_1} \times ... \times Z_{p_t}^{n_t}, for distinct primes p_i. We also obtain a lower bound of the form 1/(m^{2}s)^ceiling(phi(m)/2), on the absolute value of the smallest non-zero Fourier coefficient of an s-sparse function, where m=p_1 ... p_t, and phi(m)=(p_1-1) ... (p_t-1). We carefully apply probabilistic techniques from Gopalan et al., to obtain our structural results, and use some non-trivial results from algebraic number theory to get the lower bound. We construct a family of at most s-sparse Boolean functions over Z_p^n, where p > 2, for arbitrarily large enough s, where the minimum non-zero Fourier coefficient is 1/omega(n). The "Granularity" result of Gopalan et al. implies that the absolute values of non-zero Fourier coefficients of any s-sparse Boolean valued function over Z_2^n are 1/O(s). So, our result shows that one cannot expect such a lower bound for general Abelian groups. Using our new structural results on the Fourier coefficients of sparse functions, we design an efficient testing algorithm for Fourier-sparse Boolean functions, thata requires poly((ms)^phi(m),1/epsilon)-many queries. Further, we prove an Omega(sqrt{s}) lower bound on the query complexity of any adaptive sparsity testing algorithm.

Published
2024

5. EchoNet-Synthetic: Privacy-preserving Video Generation for Safe Medical Data Sharing

Author

Reynaud, Hadrien, Meng, Qingjie, Dombrowski, Mischa, Ghosh, Arijit, Day, Thomas, Gomez, Alberto, Leeson, Paul, and Kainz, Bernhard

Subjects
Computer Science - Computer Vision and Pattern Recognition
Abstract

To make medical datasets accessible without sharing sensitive patient information, we introduce a novel end-to-end approach for generative de-identification of dynamic medical imaging data. Until now, generative methods have faced constraints in terms of fidelity, spatio-temporal coherence, and the length of generation, failing to capture the complete details of dataset distributions. We present a model designed to produce high-fidelity, long and complete data samples with near-real-time efficiency and explore our approach on a challenging task: generating echocardiogram videos. We develop our generation method based on diffusion models and introduce a protocol for medical video dataset anonymization. As an exemplar, we present EchoNet-Synthetic, a fully synthetic, privacy-compliant echocardiogram dataset with paired ejection fraction labels. As part of our de-identification protocol, we evaluate the quality of the generated dataset and propose to use clinical downstream tasks as a measurement on top of widely used but potentially biased image quality metrics. Experimental outcomes demonstrate that EchoNet-Synthetic achieves comparable dataset fidelity to the actual dataset, effectively supporting the ejection fraction regression task. Code, weights and dataset are available at https://github.com/HReynaud/EchoNet-Synthetic., Comment: Accepted at MICCAI 2024

Published
2024

6. A Hanani-Tutte Theorem for Cycles

Author

Chakraborty, Sutanoya and Ghosh, Arijit

Subjects
Mathematics - Combinatorics
Abstract

Given a drawing $D$ of a graph $G$, we define the crossing number between any two cycles $C_{1}$ and $C_{2}$ in $D$ to be the number of crossings that involve at least one edge from each of $C_1$ and $C_2$ except the crossings between edges that are common to both cycles. We show that if the crossing number between every two cycles in $G$ is even in a drawing of $G$ on the plane, then there is a planar drawing of $G$. This result can be extended to arbitrary surfaces. We also establish an equivalence between our result and a fundamental result due to Cairns-Nikolayevsky and Pelsmajer-Schaefer-\v{S}tefankovi\v{c}, about drawing graphs on surfaces, and derive the Loebl-Masbaum theorem from it., Comment: Included equivalence with an established result, and derived a previous theorem from the result

Published
2024

7. Near Uniform Triangle Sampling Over Adjacency List Graph Streams

Author

Bishnu, Arijit, Ghosh, Arijit, Mishra, Gopinath, and Sen, Sayantan

Subjects
Computer Science - Data Structures and Algorithms
Abstract

Triangle counting and sampling are two fundamental problems for streaming algorithms. Arguably, designing sampling algorithms is more challenging than their counting variants. It may be noted that triangle counting has received far greater attention in the literature than the sampling variant. In this work, we consider the problem of approximately sampling triangles in different models of streaming with the focus being on the adjacency list model. In this problem, the edges of a graph $G$ will arrive over a data stream. The goal is to design efficient streaming algorithms that can sample and output a triangle from a distribution, over the triangles in $G$, that is close to the uniform distribution over the triangles in $G$. The distance between distributions is measured in terms of $\ell_1$-distance. The main technical contribution of this paper is to design algorithms for this triangle sampling problem in the adjacency list model with the space complexities matching their counting variants. For the sake of completeness, we also show results on the vertex and edge arrival models., Comment: 26 pages

Published
2024

10. Countably Colorful Hyperplane Transversal

Author

Chakraborty, Sutanoya, Ghosh, Arijit, and Nandi, Soumi

Subjects
Mathematics - Combinatorics, Computer Science - Computational Geometry, 52A35
Abstract

Let $\left\{ \mathcal{F}_{n}\right\}_{n \in \mathbb{N}}$ be an infinite sequence of families of compact connected sets in $\mathbb{R}^{d}$. An infinite sequence of compact connected sets $\left\{ B_{n} \right\}_{n\in \mathbb{N}}$ is called heterochromatic sequence from $\left\{ \mathcal{F}_{n}\right\}_{n \in \mathbb{N}}$ if there exists an infinite sequence $\left\{ i_{n} \right\}_{n\in \mathbb{N}}$ of natural numbers satisfying the following two properties: (a) $\{i_{n}\}_{n\in \mathbb{N}}$ is a monotonically increasing sequence, and (b) for all $n \in \mathbb{N}$, we have $B_{n} \in \mathcal{F}_{i_n}$. We show that if every heterochromatic sequence from $\left\{ \mathcal{F}_{n}\right\}_{n \in \mathbb{N}}$ contains $d+1$ sets that can be pierced by a single hyperplane then there exists a finite collection $\mathcal{H}$ of hyperplanes from $\mathbb{R}^{d}$ that pierces all but finitely many families from $\left\{ \mathcal{F}_{n}\right\}_{n \in \mathbb{N}}$. As a direct consequence of our result, we get that if every countable subcollection from an infinite family $\mathcal{F}$ of compact connected sets in $\mathbb{R}^{d}$ contains $d+1$ sets that can be pierced by a single hyperplane then $\mathcal{F}$ can be pierced by finitely many hyperplanes. To establish the optimality of our result we show that, for all $d \in \mathbb{N}$, there exists an infinite sequence $\left\{ \mathcal{F}_{n}\right\}_{n \in \mathbb{N}}$ of families of compact connected sets satisfying the following two conditions: (1) for all $n \in \mathbb{N}$, $\mathcal{F}_{n}$ is not pierceable by finitely many hyperplanes, and (2) for any $m \in \mathbb{N}$ and every sequence $\left\{B_n\right\}_{n=m}^{\infty}$ of compact connected sets in $\mathbb{R}^d$, where $B_i\in\mathcal{F}_i$ for all $i \geq m$, there exists a hyperplane in $\mathbb{R}^d$ that pierces at least $d+1$ sets in the sequence., Comment: 23 pages, 7 figures

Published
2024

14. Stabbing boxes with finitely many axis-parallel lines and flats

Author

Chakraborty, Sutanoya, Ghosh, Arijit, and Nandi, Soumi

Subjects
Mathematics - Combinatorics, Computer Science - Computational Geometry, 52A35
Abstract

In this short note, we provide the necessary and sufficient condition for an infinite collection of axis-parallel boxes in $\mathbb{R}^{d}$ to be pierceable by finitely many axis-parallel $k$-flats, where $0 \leq k < d$. We also consider colorful generalizations of the above result and establish their feasibility. The problem considered in this paper is an infinite variant of the Hadwiger-Debrunner $(p, q)$-problem., Comment: 17 pages and 2 figures

Published
2023
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15. Dimension Independent Helly Theorem for Lines and Flats

Author

Chakraborty, Sutanoya, Ghosh, Arijit, and Nandi, Soumi

Subjects
Mathematics - Combinatorics, Computer Science - Computational Geometry, 52A35
Abstract

We give a generalization of dimension independent Helly Theorem of Adiprasito, B\'{a}r\'{a}ny, Mustafa, and Terpai (Discrete & Computational Geometry 2022) to higher dimensional transversal. We also prove some impossibility results that establish the tightness of our extension., Comment: 10 pages

Published
2023

16. Linear isomorphism testing of Boolean functions with small approximate spectral norm

Author

Ghosh, Arijit, Kayal, Chandrima, Paraashar, Manaswi, and Roy, Manmatha

Subjects
Computer Science - Computational Complexity
Abstract

Two Boolean functions f, g : F_2^{n} \to {-1, 1} are called linearly isomorphic if there exists an invertible matrix M \in F_2^{n\times n} such that f\circ M = g. Testing linear isomorphism is a generalization of, now classical in the context of property testing, isomorphism testing between Boolean functions. Linear-invariance of Boolean functions has also been extensively studied in other areas like coding theory and cryptography, and mathematics in general. In this paper, we will study the following two variants of this problem: [1] [Communication complexity: ] Assume that Boolean functions f and g on F_2^{n} are given to Alice and Bob respectively, and the goal is to test linear isomorphism between f and g by exchanging a minimum amount of communication, measured in bits, between Alice and Bob. Our main result is an efficient two-party communication protocol for testing linear isomorphism in terms of the approximate spectral norm of the functions. We will crucially exploit the connection between approximate spectral norm and sign-approximating polynomials. [2] [Query complexity: ] If f: F_2^{n} \to { -1, 1 } is a known function and g : F_2^{n} \to { -1, 1 } be an unknown function with a query access. We study the query complexity of testing linear isomorphism between f and g in terms of the approximate spectral norm of f. As in the case of communication complexity, we will use properties of the approximate spectral norm.

Published
2023

18. On higher multiplicity hyperplane and polynomial covers for symmetry preserving subsets of the hypercube

Author

Ghosh, Arijit, Kayal, Chandrima, Nandi, Soumi, and Venkitesh, S.

Subjects
Mathematics - Combinatorics
Abstract

Alon and F\"uredi (European J. Combin. 1993) gave a tight bound for the following hyperplane covering problem: find the minimum number of hyperplanes required to cover all points of the n-dimensional hypercube {0,1}^n except the origin. Their proof is among the early instances of the polynomial method, which considers a natural polynomial (a product of linear factors) associated to the hyperplane arrangement, and gives a lower bound on its degree, whilst being oblivious to the (product) structure of the polynomial. Thus, their proof gives a lower bound for a weaker polynomial covering problem, and it turns out that this bound is tight for the stronger hyperplane covering problem. In a similar vein, solutions to some other hyperplane covering problems were obtained, via solutions of corresponding weaker polynomial covering problems, in some special cases in the works of the fourth author (Electron. J. Combin. 2022), and the first three authors (Discrete Math. 2023). In this work, we build on these and solve a hyperplane covering problem for general symmetric sets of the hypercube, where we consider hyperplane covers with higher multiplicities. We see that even in this generality, it is enough to solve the corresponding polynomial covering problem. Further, this seems to be the limit of this approach as far as covering symmetry preserving subsets of the hypercube is concerned. We gather evidence for this by considering the class of blockwise symmetric sets of the hypercube (which is a strictly larger class than symmetric sets), and note that the same proof technique seems to only solve the polynomial covering problem.

Published
2023

19. Sparse Geometric Set Systems and the Beck-Fiala Conjecture

Author

Dutta, Kunal and Ghosh, Arijit

Subjects
Computer Science - Computational Geometry
Abstract

We investigate the combinatorial discrepancy of geometric set systems having bounded shallow cell complexity in the \emph{Beck-Fiala} setting, where each point belongs to at most $t$ ranges. For set systems with shallow cell complexity $\psi(m,k)=g(m)k^{c}$, where $(i)$ $g(m) = o(m^{\varepsilon})$ for any $\varepsilon\in (0,1],$ $(ii)$ $\psi$ is non-decreasing in $m$, and $(iii)$ $c>0$ is independent of $m$ and $k$, we get a discrepancy bound of \[ O\left(\sqrt{\left(\log n+\left(t^{c}g(n)\right)^{\frac{1}{1+c}}\right)\log n}\right).\] For $t=\omega(\log^2 n)$, in several cases, such as for set systems of points and half-planes / disks / pseudo-disks in $\mathbb{R}^2$, points and orthants in $\mathbb{R}^3$ etc., these bounds are $o(\sqrt{t})$, which verifies (and improves upon) the conjectured bound of Beck and Fiala~\emph{(Disc. Appl. Math., 1981)}. Our bounds are obtained by showing the existence of \emph{matchings with low crossing number}, using the multiplicative weights update method of Welzl \emph{(SoCG, 1988)}, together with the recent bound of Mustafa \emph{(Disc. Comp. Geom., 2015)} on \emph{shallow packings} of set systems in terms of their shallow cell complexity. For set systems of shallow cell complexity $\psi(m,k)=m^{c_1}g(m)k^{c}$, we obtain matchings with crossing number at most \[ O\left(\left(n^{c_1}g(n)t^{c}\right)^{\frac{1}{1+c_1+c}}\right).\] These are of independent interest.

Published
2023

20. Heterochromatic Geometric Transversals of Convex sets

Author

Chakraborty, Sutanoya, Ghosh, Arijit, and Nandi, Soumi

Subjects
Mathematics - Combinatorics, Computer Science - Computational Geometry, 52A35, G.2.m
Abstract

An infinite sequence of sets $\left\{B_{n}\right\}_{n\in\mathbb{N}}$ is said to be a heterochromatic sequence from an infinite sequence of families $\left\{ \mathcal{F}_{n} \right\}_{n \in \mathbb{N}}$, if there exists a strictly increasing sequence of natural numbers $\left\{ i_{n}\right\}_{n \in \mathbb{N}}$ such that for all $n \in \mathbb{N}$ we have $B_{n} \in \mathcal{F}_{i_{n}}$. In this paper, we have proved that if for each $n\in\mathbb{N}$, $\mathcal{F}_n$ is a family of {\em nicely shaped} convex sets in $\mathbb{R}^d$ such that each heterochromatic sequence $\left\{B_{n}\right\}_{n\in\mathbb{N}}$ from $\left\{ \mathcal{F}_{n} \right\}_{n \in \mathbb{N}}$ contains at least $k+2$ sets that can be pierced by a single $k$-flat ($k$-dimensional affine space) then all but finitely many families in $\left\{\mathcal{F}_{n}\right\}_{n\in \mathbb{N}}$ can be pierced by finitely many $k$-flats. This result can be considered as a {\em countably colorful} generalization of the $(\aleph_0, k+2)$-theorem proved by Keller and Perles (Symposium on Computational Geometry 2022). We have also established the tightness of our result by proving a number of no-go theorems., Comment: 17 pages and 5 figures

Published
2022

21. Relationship Between Severity of Ischemia and Coronary Artery Disease for Different Stress Test Modalities in the ISCHEMIA Trial

Author

Reynolds, Harmony R., Page, Courtney B., Shaw, Leslee J., Berman, Daniel S., Chaitman, Bernard R., Picard, Michael H., Kwong, Raymond Y., Min, James K., Leipsic, Jonathon, Mancini, G.B. John, Budoff, Matthew J., Hague, Cameron J., Senior, Roxy, Szwed, Hanna, Bhargava, Balram, Celutkiene, Jelena, Gadkari, Milind, Bainey, Kevin R., Doerr, Rolf, Ramos, Ruben B., Ong, Peter, Naik, Sudhir R., Steg, Philippe Gabriel, Goetschalckx, Kaatje, Chow, Benjamin J.W., Scherrer-Crosbie, Marielle, Phillips, Lawrence, Mark, Daniel B., Spertus, John A., Alexander, Karen P., O’Brien, Sean M., Boden, William E., Bangalore, Sripal, Stone, Gregg W., Maron, David J., Hochman, Judith S., Mavromatis, Kreton, Linefsky, Jason, Miller, Todd, Banerjee, Subhash, Newman, Jonathan D., Donnino, Robert M., Saric, Muhamed, Abdul-Nour, Khaled, Stone, Peter H., Jang, James J., Yee, Gennie, Weitz, Steven, Arnold, Suzanne, James Henry, O’Keefe, Jr, Shapiro, Michael D., Fein, Steven A., Torosoff, Mikhail T., Lyubarova, Radmila, Mookherjee, Sulagna, Drzymalski, Krzysztof, McFalls, Edward O., Garcia, Santiago A., Bertog, Stefan C., Siddiqui, Rizwan A., Ishani, Areef, Hansen, Ronnell A., Georges Khouri, Michel, Goldberg, Jonathan L., Goldweit, Richard, Cohen, Ronny A., Mirrer, Brooks, Navarro, Victor, Winchester, David E., Kronenberg, Marvin, McFarren, Christopher, Heitner, John F., Dauber, Ira M., Cannan, Charles, Sudarshan, Sriram, Mehta, Puja K., McDaniel, Michael, Lerakis, Stamatios, Quyyumi, Arshed, Wenger, Nanette K., Hedgepeth, Chester M., Hurlburt, Heather, Rosen, Alan, Sahul, Zakir, Leung, Steve, Reda, Hassan, Ziada, Khaled, Setty, Sampoornima, Barua, Rajat S., Hage, Fadi, Davies, James E., Leesar, Massoud, Heo, Jaekyeong, Iskandrian, Amy, Al Solaiman, Firas, Singh, Satinder, Dajani, Khaled, El-Hajjar, Mohammad, Der Mesropian, Paul, Sacco, Joseph, McCandless, Brian, Orgera, Marisa, Sidhu, Mandeep S., Arif, Imran, Kerr, Hanan, Trejo (Gutierrez), Jorge F., Fletcher, Gerald, Lane, Gary E., Neeson, Lynn M., Parikh, Pragnesh P., Pollak, Peter M., Shapiro, Brian P., Landolfo, Kevin, Gemignani, Anthony, OʼRourke, Daniel, Meadows, Judith L., Call, Jason T., Hannan, Joseph, Bojar, Robert, Kumar, Deepti, Mukai, John, Martin, Edward T., Vorobiof, Gabriel, Moorman, Alec, Kinlay, Scott, Hamburger, Robert J., Rocco, Thomas P., Bhatt, Deepak L., Croce, Kevin, Quin, Jacquelyn A., Anumpa, Jati, Zenati, Marco, Faxon, David P., Rayos, Glenn, Seedhom, Ashraf, Sullenberger, Lance, Kumkumian, Gregory, Sedlis, Steven P., Donnino, Robert M., Lorin, Jeffrey, Tamis-Holland, Jacqueline E., Kornberg, Robert, Leber, Robert, Saba, Souheil, Lee, Michael W., Small, Delano R., Nona, Wassim, Alexander, Patrick B., Rehman, Iram, Badami, Umesh, Marzo, Kevin, Robbins, Inga H., Levite, Howard A., Shetty, Sanjay, Patel, Mayuri, Hamroff, Glenn S., Little, Raymond W., Zimbelman, Brandi D., Lui, Charles Y., Smith, Brigham R., Vezina, Daniel P., Khor, Lillian L., Abraham, Josephine D., Bull, David A., McKellar, Stephen H., Booth, David, Kotter, John, Abdel-Latif, Ahmed, Hu, Bob, Labovitz, Arthur J., Berlowitz, Michael, Rogal, Philip, Matar, Fadi, Caldeira, Christiano, Rodriguez, Fatima, Schnittger, Ingela, Fearon, William F., Deedwania, Prakash, Reddy, Kiran, Sweeny, Joseph, Spizzieri, Christopher, Hochberg, Claudia P., Salerno, William D., Wyman, Ray, Zarka, Amer, Shah, Anil V., Haldis, Thomas, Kohn, Jeffrey A., Girotra, Saket, Almousalli, Omar, Krishnam, Mayil S., Milliken, Jeffrey C., Patel, Pranav M., Seto, Arnold H., Harley, Kevin T., Gibson, Michael A., Allen, Byron J., Coram, Rita, Thomas, Sabu, Schwartz, Ronald G., Chen, Wei, El Shahawy, Mahfouz, Stafford, James, Abernethy, William B., Zurick, Andrew, Meyer, Thomas M., Morford, Ronald G., Rutkin, Bruce, Bokhari, Sabahat, Sokol, Seth I., Meisner, Jay, Hamzeh, Ihab, Misra, Arunima, Matthew, Wall, Jr, De Rosen, Veronica Lenges, Alam, Mahboob, Turner, Michael C., Mulhearn, Thomas J., Good, Arnold P., Shammas, Nicolas W., Chilton, Robert, Nguyen, Patricia K., Jezior, Matthew, Gordon, Paul C., Crain, Thomas, Stenberg, Robert, Pedalino, Ronald P., Wiesel, Joseph, Juang, George J., Al-Amoodi, Mohammed, Wohns, David, Lader, Ellis W., Mumma, Michael, Dharmarajan, Lekshmi, Joseph F.X., McGarvey, Jr, Downes, Thomas R., Luckasen, Gary J., Cheong, Benjamin, Potluri, Srinivasa, Mastouri, Ronald A., Breall, Jeffery A., Revtyak, George E., Bazeley, Jonathan W., Li, Dayuan, Giedd, Kenneth, Old, Wayne, Burt, Francis, Sokhon, Kozhaya, Gopal, Deepika, Valeti, Uma S., Kobashigawa, Jon, Chakanalil Govindan, Sajeev, Gopalan Nair, Rajesh, Nanjappa Manjunath, Cholenahally, Moorthy, Nagaraja, Cholenahally Manjunath, Satvic, Narayanappa, Suryaprakash, Pandit, Neeraj, Kumar Nath, Ranjit, Dwivedi, S.K., Narain, V.S., Chandra, Sharad, Wander, Gurpreet S., Tandon, Rohit, Ralhan, Sarju, Aslam, Naved, Goyal, Abhishek, Karthikeyan, G., Ramakrishnan, S., Seth, Sandeep, Yadav, Rakesh, Singh, Sandeep, Roy, Ambuj, Parakh, Neeraj, Kumar Verma, Sunil, Narang, Rajiv, Mishra, Sundeep, Naik, Nitish, Sharma, Gautam, Kumar Choudhary, Shiv, Patel, Chetan, Gulati, Gurpreet, Sharma, Sanjeev, Bahl, V.K., Mathew, Anoop, Punnoose, Eapen, Gadage, Siddharth, Umesh Pillay, Tapan, Satheesh, Santhosh, Mathur, Atul, Christopher, Johann, Menon, Rajeev, Kumar, Nirmal, Oomman, Abraham, Mao, Robert, Solomon, Hilda, Parveen Khan, Sajeeda, Grant, Purvez, Kachru, Ranjan, VK, Ajit Kumar, Ganapathi, Sanjay, K., Jayakumar, Sivadasanpillai, Harikrishnan, Sasidharan, Bijulal, T.R., Kapilamoorthy, Polamuri, Praneeth, Kaul, Upendra, Fox, Keith A.A., Carruthers, Kathryn, Elghamaz, Ahmed, Gurunathan, Sothinathan, Karogiannis, Nikolaos, Shah, Benoy N., Trimlett, Richard H.J., Rubens, Michael B., Nicol, Edward D., Mittal, Tarun K., Hampson, Reinette, Andreas Gamma, Reto, de Belder, Mark A., Thambyrajah, Jeet, Nageh, Thuraia, Davies, John R., Lindsay, Steven J., Kurian, John, Jamil, Haqeel, Raheem, Osama, Hoye, Angela, Donnelly, Patrick, Valec ka, Bernardas, Chauhan, Anoop, Barr, Craig, Alfakih, Khaled, Byrne, Jonathan, Webb, Ian, Henriksen, Peter, O. Kane, Peter, de Silva, Ramesh, Conway, Dwayne S.G., Sirker, Alexander A., Hoole, Stephen P., Witherow, Fraser N., Johnston, Nicola, Harbinson, Mark, Walsh, Simon, Douglas, Hanna, Luckie, Matthew, Sobolewska, Jolanta, Jeetley, Paramjit, Patel, Niket, Kotecha, Tushar, Travill, Christopher, Karimullah, Iqbal, Al-Bustami, Mahmud, Braganza, Denise, Henderson, Robert, Pointon, Kate, Naik, Surendra, Mathew, Thomas, Berry, Colin, Collison, Damien, Roditi, Giles, Moriarty, Andrew J., Glover, Jason D., Pradhan, Jiwan, Ghada, Mikhail, Francis, Darrel P., Dzavik, Vladimir, Diaz, Ariel, Rheault, Philippe, Barrero, Miguel, Gagné, Carl-Éric, Pépin-Dubois, Yanek, Costa, Ricardo, Tung Sia, Ying, Lemay, Catherine, Gisbert, Alejandro, Gervais, Pierre, Rheault, Alain, Carl Phaneuf, Denis, Gosselin, Gilbert, Garg, Pallav, Hessian, Renee C., Beanlands, Rob S., Davies, Richard F., Cheema, Asim N., Bagai, Akshay, Wald, Ron, Goodman, Shaun, Graham, John Joseph, Peterson, Mark, Chow, Chi-Ming, Abramson, Beth, Nazir Cheema, Asim, Tariq Vakani, Mohammad, Cha, James, Howarth, Andrew G., Wong, Graham, Uxa, Amar, Galiwango, Paul, Kassam, Saleem, Mukherjee, Ashok, Joseph Ricci, A., Lam, Andy, Me, Shamir, Udell, Jacob, Généreux, Philippe, Hameed, Adnan, Daba, Ledjalem, Hueb, Whady, Cury Rezende, Paulo, Ciappina Hueb, Alexandre, Emanuela, Paola, Smanio, Poggio, Schaan de Quadros, Alexandre, Abdala, Renato, Kalil, Karam, da Costa Vieira, José Luiz, Grossmann, Gabriel, Píccaro de Oliveira, Pedro, Bridi, Leonardo, Savaris, Simone, Vitola, João V., Cerci, Rodrigo J., Farias, Fabio R., Fernandes, Miguel M., Antonio Marin-Neto, José, Schmidt, André, de Oliveira Lima Filho, Moysés, Mendes Oliveira, Ricardo, Reynaldo, João, Chierice, Abbud, Polanczyk, Carísi A., Furtado, Mariana V., Smidt, Luis F., Carlos Carvalho, Antonio, Pucci, Gustavo, Lyra, Flavio, Rabelo, Alvaro, Junior, Alves, Dracoulakis, Marianna D.A., Lima, Rodolfo G.S.D., Figueiredo, Estevao, Ricardo Caramori, Paulo, Tumelero, Rogerio, Dall’Orto, Frederico, Mesquita, Claudio T., Colafranseschi, Alexandre S., Amarino C., Oliveira, Jr, Carvalho, Luiz A., Palazzo, Isabella C., Sousa, Andre S., da Silva, Expedito Eustáquio Ribeiro, Gabriel, Pedro, de Barros e Silva, Melo, de Pádua Silva Baptista, Luciana, Jamus Rodrigues, Marcelo, de Resende, Marcos Valério Coimbra, Francisco Saraiva, Jose, Costantini, Costantino, Ruzyllo, Witold, Demkow, Marcin, Pracon, Radoslaw, Kepka, Cezary, Teresinska, Anna, Kryczka, Karolina, Henzel, Jan, Solecki, Mateusz, Kaczmarska, Edyta, Mazurek, Tomasz, Drozdz, Jaroslaw, Czarniak, Bartosz, Frach, Malgorzata, Szymczyk, Konrad, Niedzwiecka, Iwona, Sobczak, Sebastian, Ciurus, Tomasz, Jakubowski, Piotr, Misztal-Teodorczyk, Magdalena, Teodorczyk, Dawid, Fratczak, Aleksandra, Szkopiak, Marcin, Lebioda, Patrycja, Wlodarczyk, Michal, Plachcinska, Anna, Kusmierek, Jacek, Miller, Magdalena, Marciniak, Halina, Wojtczak-Soska, Karolina, Łuczak, Katarzyna, Tarchalski, Tomasz, Cichocka-Radwan, Anna, Anna Szulczyk, Grazyna, Witkowski, Adam, Kukuła, Krzysztof, Celińska-Spodar, Małgorzta, Zalewska, Joanna, Gajos, Grzegorz, Bury, Krzysztof, Pruszczyk, Piotr, Roik, Marek, Łoboz-Grudzień, Krystyna, Sokalski, Leszek, Brzezińska, Barbara, Lesiak, Maciej, Łanocha, Magdalena, Reczuch, Krzysztof W., Kalarus, Zbigniew, Swiatkowski, Andrzej, Szulik, Mariola, Musial, Wlodzimierz J., Bockeria, Leo, Petrosyan, Karen, Trifonova, Tatiana, Chernyavskiy, Alexander M., Kretov, Evgeniy I., Grazhdankin, Igor O., Bershtein, Leonid L., Sayganov, Sergey A., Kuzmina-Krutetskaya, Anastasia M., Zbyshevskaya, Elizaveta V., Katamadze, Nana O., Demchenko, Elena A., Kozlov, Pavel S., Kozulin, Vikentiy Y., Lubinskaya, Ekaterina I., Lopez-Sendon, Jose, Castro, Almudena, Refoyo Salicio, Elena, Guzman, Gabriela, Galeote, Gabriel, Valbuena, Silvia, Peteiro, Jesús, Dolores Martínez-Ruíz, María, Pérez-Fernández, Ruth, Cuenca-Castillo, José J., Flores-Ríos, Xacobe, Prada-Delgado, Óscar, Barge-Caballero, Gonzalo, Ramon Gonzalez Juanatey, Jose, Souto Bayarri, Miguel, Pubull Nuñez, Virginia, Ocaranza Sanchez, Raymundo, Cid Alvarez, Belen, Peña Gil, Carlos, Martinez Monzonis, Amparo, Sionis, Alessandro, Vila Perales, Montserrat, Maria Padró, Josep, Serra Peñaranda, Antonio, García Picart, Joan, Ginel Iglesias, Antonino, Garcia-Moll Marimon, Xavier, Pons Lladó, Guillem, Carreras Costa, Francesc, Miro, Vicente, Diez, Jose L., Calvillo, Pilar, Marin Ortuño, F., Valdés Chávarri, M., Tello Montolliu, A., Pinar Bermudez, E., De La Morena, G., Gracida Blancas, Montserrat, Enrique Castillo Luena, Jose, Fernandez-Aviles, Francisco, Chen, Jiyan, Wu, Yongjian, Ma, Yitong, Yang, Yining, Ji, Zheng, Yang, Xinchun, Lin, Wenhua, Zeng, Hesong, Fu, Xin, Wang, Songtao, Cheng, Gong, Zhao, Yulan, Fang, Xuehua, Zeng, Qiutang, Su, Xi, Li, Qingxian, Nie, Shao-Ping, Yu, Qin, Wang, Jianʼan, Zhang, Shuyang, Liu, Zhenyu, Maggioni, Aldo P., Piero Perna, Gian, Marini, Marco, Gabrielli, Gabriele, Provasoli, Stefano, Verna, Edoardo, Monti, Lorenzo, Nardi, Barbara, Di Chiara, Antonio, Mortara, Andrea, Galvani, Marcello, Ottani, Filippo, Sicuro, Marco, Calabro, Paolo, Formisano, Tiziana, Tarantini, Giuseppe, Cucchini, Umberto, Luigi Andres, Anto, Racca, Emanuela, Briguori, Carlo, Amati, Roberto, Vergoni, William, Russo, Aldo, Fanelli, Raffaele, Poh, Kian-Keong, Chai, Ping, Lau, Titus, Loh, Joshua P., Tay, Edgar L., Teoh, Kristine, Teo, Lynette L., Ong, Ching-Ching, Wong, Raymond C., Loh, Poay-Huan, Kofidis, Theodoros, Xian Chan, Wan, Hui Chan, Koo, Foo, David, Loh Kwok Kong, Jason, Ching, Min, Er, Haider Jafary, Fahim, Chua, Terrance, Stumpf, Juergen, Matschke, Klaus, Simonis, Gregor, Kadalie, Clemens T., Sechtem, Udo, Christian Schulze, P., Goebel, Bjoern, Lenk, Karsten, Nickenig, Georg, Schuchlenz, Herwig, Weikl, Stefan, Marthe Lang, Kurt Huber, Irene, Jakl-Kotauschek, Gabriele, Vertes, Matyas Keltai Andras, Varga, Albert, Fontos, Geza, Merkely, Bela, Kerecsen, Gabor, Hinic, Sasa, Zdravkovic, Marija, Mudrenovic, Vladan, Crnokrak, Bogdan, Beleslin, Branko D., Boskovic, Nikola N., Petrovic, Marija T., Dobric, Milan R., Markovic, Zeljko Z., Mladenovic, Ana S., Cemerlic-Adjic, Nada, Davidović, Goran, Vučić, Rada, Nikola Dekleva, Milica, Stankovic, Goran, Apostolovic, Svetlana, Escobedo, Jorge, Baleón-Espinosa, Rubén, Campos-Santaolalla, Arturo S., Durán-Cortés, Elihú, Flores-Palacios, José M., García-Rincón, Andrés, Jiménez-Santos, Moisés, Peñafiel, Joaquín V., Ortega-Ramírez, José A., Valdespino-Estrada, Aquiles, Alexánderson Rosas, Erick, Murphy, Deirdre, Selvanayagam, Joseph B., Joseph, Majo X., Thambar, Suku T., Rankin, Jamie, Beltrame, John F., Hillis, Graham S., Thuaire, Christophe, Dutoiu, Téodora, Juliard, Jean-Michel, Slama, Michel S., El Mahmoud, Rami, Nicollet, Eric, Goube, Pascal, Barone-Rochette, Gilles, Furber, Alain, Bière, Loïc, Laucevicius, Elvin Kedhi, Aleksandras, Timmer, MD Jorik, Hermanides, Rik, Kaplan, Eliza, Riezebos, Robert K., Samadi, Pouneh, van Dongen, Elise, Niehe, Sander R., Suryapranata, Harry, van Vugt, Stijn, Cacela, Duarte, Santana, Ana, Fiarresga, Antonio, Sousa, Lidia, Marques, Hugo, Patricio, Lino, Bernanrdes, Luis, Rio, Pedro, Carvalho, Ramiro, Ferreira, Rui, Silva, Tiago, Rodrigues, Ines, Modas, Pedro, Portugal, Guilherme, Fragata, Jose, Pinto, Fausto J., Nobre Menezes, Miguel, Cantinho Lopes, Guilhermina, Gomes Almeida, Ana, Canas Silva, Pedro, Nobre, Angelo, Rita Francisco, Ana, Ferreira, Nuno, Lopes, Ricardo L., Diaz, Rafael, Guzman, Luis, César Figal, Julio, Méndiz, Oscar, Cortés, Claudia, René Favaloro, Roberto, Alvarez, Carlos, Courtis, Javier, Zeballos, Gabriela, Schiavi, Lilia, Rubio, Mariano, Alsweiler, Caroline, Patrick Devlin, Gerard, Fisher, Raewyn, Alan Huston Stewart, Ralph, Douglas White, Harvey, Benatar, Jocelyne, Kedev, Sasko, Peovska Mitevska, Irena, Srbinovska Kostovska, Elizabeta, Pejkov, Hristo, Held, Claes, Eggers, Kai, Frostfelt, Gunnar, Johnston, Nina, Olsowka, Maciej, Åkerblom, Axel, Soveri, Inga, Aspberg, Johannes, Beyar, Rafael, Nikolsky, Eugenia, Sharir, Tali, Elian, Dan, Kerner, Arthur, Massalha, Samia, Fukuda, Keiichi, Kohsaka, Shun, Yasuda, Satoshi, Nishimura, Shigeyuki, Van de Werf, Frans, Claes, Kathleen, Hung, Chung-Lieh, Yun, Chun-Ho, Jia-Yin Hou, Charles, Kuo, Jen-Yuan, Yeh, Hung-I, Hung, Ta-Chuan, Li, Jiun-Yi, Chien, Chen-Yen, Tsai, Cheng-Ting, Liu, Chun-Chieh, Yu, Fa-Chang, Lin, Yueh-Hung, Lan, Wei-Ren, Yen, Chih-Hsuan, Tsai, Jui-Peng, Sung, Kuo-Tzu, Ntsekhe, Mpiko, Pandie, Shaheen, Viljoen, Charle A., De Andrade, Marianne, Moccetti, Tiziano, Grazia Rossi, M., Abdelhamid, Magdy, Adel, Ahmed, Kamal, Ahmed, Mahrous, Hossam, El Kaffas, Sameh, El Fishawy, Hussien, Pop, Calin, Claudia, Matei, Popescu, Bogdan A., Ginghina, Carmen, Deleanu, Dan, Iliescu, Vlad A., Al-Mallah, Mouaz H., Aljzeeri, Ahmed, Najm, Hani, Alghamdi, Ali, Ramos, Walter Enrique Mogrovejo, Kuanprasert, Srun, Prommintikul, Arintaya, Nawarawong, Weerachai, Woragidpoonpol, Surin, Tepsuwan, Thitipong, Taksaudom, Noppon, Rimsukcharoenchai, Chataroon, Euathrongchit, Juntima, Wannasopha, Yutthaphan, Yamwong, Sukit, Sritara, Piyamitr, Aramcharoen, Suthara, Meemuk, Krissada, Khairuddin, Ahmad, Abd Hadi, Hafidz, Azmi Yahaya, Shaiful, Doan, John, Lee, Raven, Patel, Risha, Yang Cho, So, Milbrandt, Susan, Shelstad, Dawn, Kamath, Preeti, Tejani, Ishita, Quiles, Kirsten J., Schley, Allison, Golden, Heather, Osseni, Hermine, Wiyarand, Charlene, Douglass, Peter, Pomeroy, Hayley, Craft, Alexandra, Harvey, Bethany, Anaya, Olivia, Goold, Phoebe, Giovannone, Steven, Pritchard, Lori, Gans Paul Kennedy, Rosann, Ganesan, Shobana, Schlichting, David, Naher, Aynun, Stewart, Wendy L., Salmi, Kristin M., Johnson, Debra K., Herrmann, Rebekah R., Arges, Kristine, LeFevre, Melissa, Tomfohr, Jennifer, Ann Byrne, Kimberly, Zappernick, Taissa, Canada, Sallie, Kakade, Meghana, Mieses, Patricia, Cobos, Stanley E., Dwyer, Raven R., Espinosa, Dalisa, Quiles, Kirsten J., Rantinella, Magdalena, Rodriguez, Jessica, Mancilla, Olivia, Stinson, Susan, Weyand, Terry, Crook, Sherron C., Ho, Jean, Khan, Saadat, Mohamed, Mahmoud, Soltau, Mary R., Rose, Delsa K., Wimmer, Rebecca J., Desire, Sukie, Rashid, Fauzia, Asier, Senait, Patel, Keyur, Gillis, Jennifer, Manocchia, Megan, Moore, Susan, Congdon, Elizabeth, Brandt, Gail, Marchelletta, Nora, Wippler, Kristina, Halverson, Kimberly E., Roraff, Christine, Thorsen, Jonean, Ojajuni, Amarachi, Olurinde, Oni, Surineni, Kamalakar, Valaiyapathi, Badhma, Kartje, Carol M., Rawlins, Michele, Thomson, Jennifer, Colleen Rogge, Mary, Bunke, Julie, Unterbrink, Kendra, Fannon, Jacqueline, Burman, Cynthia, Dubin, Marcia F., Beaudry, Sarah, Tirado, Stephanie A., Halliday, Janet, Julian, Stephanie, Pamela, Stanford M. Lane, Jennifer L., Arsenault, Patricia, Sigel, Pamela, Brooks, Miriam, Douangvila, Ladda, Gevorgyan, Rubine, Ranjbaran, Fatima, Smith, Bryn, Ohmart, Carly, Ly, Samantha, Quinn, Margot C., Temiyasathit, Sara, Do, Jacquelyn, Tobin, Desiree, Langdon, Jennifer, Werner Bayer, Marcia, OʼMalley, Amanda, Orvis, Erin, Murphy, Mandy, Greenberg, Ann, Iraola, Margaret, Maranan, Leandro C., Malinay, Ammy, Edillo, Candice P., Ostrander, Ann, Wasmiller, Stephanie, Drewes, Wendy, Patel, Dipti, White, Jackie M., Hallam, Alison, Spooner, Benjamin J., Hollenweger, Linda M., Little, Holly, Little, Tiffany, Eskelson, Nona A., Taul, Yvonne, Rodgers, Caroline, Isaacs, Jennifer, Bulkley, Viktoria, Kaneshiro, Renee, Kirby, Bonnie J., Tran, Nhi N., Jahrsdorfer, Catherine, Yunis, Reem, Patro, Jhina, Vega, Antonia, Bloise-Adames, Hugo, Jimenez, Santa, Saint Vrestil, Nicole, Bhandari, Reyna, Schade, Danielle, Yost, Roxanne, Beardsley, Paula, Fine, Denise, Tancredi, Jana, Arakelian, Patricia, Mathus, Susan, OʼNeill, Deborah, Burkhardt, Joy, Hosino, Suellen, Lubyanaya, Oksana A., Salas, Jose D., Aguirre, Maria, Dhawan, Manu, Parra, Diana, Tran, Tri, Fowler-Lehman, Katie, Spitzer, Natalie, Riedberger, Casey, Weick, Catherine, Quiles, Kirsten J., Drum, Carrie, Miller-Cox, Kimberly, Ollinger, Amy, Capasso-Gulve, Elizabeth, Melanie Loehr, Alaine, Mosley, Marlowe, Heydari, Shirin, Lundeen, Andrea M., Karanjah, Edgar, Marfori, Wanda C., Hernandez-Rangel, Eduardo, Singh, Pam, Marie Webb, Anne, Fridell, Ellie, Wilson, Heidi, Kim, Angela, Wilmot, Patrick, Stevens, Ramona, Black, Loriane, Hull, Amber B., Lim, Olivia J., Tucker, Helen C., Putnam, Natasha C., Hall, Linda L., Cauthren, Tia, Tucker, Trish, Horton, Hollie, Orga, Jan, White, Joyce R., Baumann, Cynthia, Seeratan, Vidya, Jimenez, Magnolia, Schultz, Cidney, Russo, Jeanne, Huda, Zohra, Boan, Araceli, Hinton, Christine R., Archer, Beth A., Dionne, Julia S., Allardyce, Cheryl A., Sikora, Lindsey N., Czerniak, Jennifer H., Mull, Jennifer A., Ferguson, Elizabeth, Laube, Frances, Shammas, Gail A., Christensen, Lori, Park, Holly, Hecht, Joan, Vo, Davis, Hirsch, James, Bindeman, Jody, Salkind, Sara, Desimone, Lori-Ann, Felix-Stern, Lina, Gomes, Jassira, Gordon, Catherine, Mann, Aimee, McCreary, Theresa, Quiles, Kirsten J., Gopaul, Candace, Hultberg, Karen, Huk, Tauqir, Hussain, Afshan, Zambrano, Yesenia, Medina Rodriguez, Sarah, Milner, Trudie, Mulder, Abbey, Van Oosterhout, Stacie, Meyer, Martha, Clapp, Nancy L., Barrentine, Heather, Jose, Jenne M., Manchery, Jenne, McKinney, Vera, Schwarz, Linda, Kaczkowski, Scott M., Jaskowiak, Adam J., Klitch, Joel, Dees, Debra, Vasquez, Precilia, Hannemann, Elise L., Mae Foltz, Judy, DeRosa, Emily, Jorgenson, Beth, Riestenberg-Smith, Joyce, Bariciano, Rebecca, Waldron, Jessica, Mayon, Michelle, Ann Peichel, Gretchen, Starks, Brandy, Garcia, Lucilla, Thottam, Maria, Anand, Anjali, Raj, Janitha, Ravindran, Reshma, Rajalekshmi, VS, Nataraj, Nandita, Bajaj, Sheromani, Yadav, Vandana, Mishra, Girish, Tewari, Roma, Mishra, Meenakshi, Patel, Shivali, Singh, Suman, Kaur, Baljeet, Gupta, Sonika, Suvarna, Chandini, Mannekkattukudy Kurian, Binoy, Rupesh Karwa, Sheetal, Kolhe, Suvarna, Vindhya, R.J., Jain, Peeyush, Seth, Ashok, Singh Meharwal, Zile, Verma, Atul, Bhatia, Mona, Sachdeva, Ankush, Indira Devi, Thounaojam, Jungla, Nungshi, Manjula Rani, K., Sowjanya Reddy, M., Preethi, K., Sidh, Rinu R., Priya, Vamshi, Preethi, Kotiboinna, Hande, Shweta, Dubey, Abhishek, Rawat, Vineeth, Kavita, Chacko, CP Manas, Babu, Suresh, Reddy, Sowjanya, Rani, Manjula, Arambam, Priyadarshani, Singh, Bebek, Young, Grace M., Kinsey, Christopher, Kavalakkat, Raisa, Evans, Jo, Hassan, Ikraam, Williams, Sarah, Holland, Kim, Swan, Karen, Atkinson, Bev, Kunhunny, Swapna, Atkinson, Craig, Krannila, Carita, Vinod, Manitha, Chaytor, Lisa, Cox, Leanne, Morrow, Julie, Rowe, Kay, Kelly, Stephanie, Regan, Susan, Turnbull, Dawn, Fleming, Catherine, Ghosh, Arijit, Gratrix, Karen, Preston, Stephen, Cartwright, Anne, Knightonc, Abigail, Martin, Katherine, Flint, Laura, Harrison, James, Lakeman, Nicki, Ljubez, Anja, Wright, Judith, Exley, Donna, Andiapen, Mervyn, Richards, Amy J., Wong, Lisa, Munro, Melanie J., McEvoy, Michelle, Brown, Caroline, Charles, Thabitha, Kolakaluri, Laurel, Phillips, Hannah, Morby, Louise, Hallett, Karen, Corbett, Carolyn, Winstanley, Lynne, Smit, Angelique, Gent, Susan, Hussain, Nafisa, Haines, Fiona, Taaffe, Joanne, Burton, Jane, Colton, Maria, King, Rachel, Brown, Ammani, Docherty, Andrew, McCloy, Lisa, Robb, Kate, Paterson, Craig, Crawford, Wenda, Kelly, Joanne, McGregor, Lorraine, Mackin, Anne, Knight, Janet P., Bose, Tuhina, Proietti, Anna, Brousseau, Myriam, Corfias, Magalie, Blaise, Patricia, Harvey, Luc, Alarie, Patricia, Arcand, Linda, Roy, Isabelle, Montpetit, Estelle, Drouin, Katia, Bergeron, Christine, Shelley, Christine, Masson, Christine, Carr, Sandy, Bone, Catherine, Moga, Ermina, Kourzenkova, Janetta, Walter, Olga, Hogg, Norma, Welsh, Suzanne, Hussain, Mohammed, Bello, Olugbenga, Syed, Ishba, Kushniriuk, Khrystyna, Otis, Judy, Otis, Rebecca, Seib, Michelle M., Rivest, Sandra M., Sandonato, Rosa, Chow, Jackie, Starovoytov, Andrew, Uchida, Naomi, Meadows, Ngaire, Asif, Nadia, Tavares, Suzana, Bozek, Bev, Shier, Maria, Larmand, Lori-Ann, Janmohamed, Amir, Hart, Brenda, Marucci, Jane, Tai, Sharon, Brons, Sonya, Beck, Chris, Wong, Glenda, Etherington, Krystal, Arumairajah, Thippeekaa, Aprile, Maria, Karlsson, Sara, Webber, Susan, Mercure, Chantale, Aedy, Nancy, Farquharson, Fran, Siddiqui, Anam, Emy Takiuti, Myrthes, Pizzol Caetano, Leonardo, Peixoto Deiro, Aline, Manica Muller, Alice, de Moraes, Maria Antonieta Pereira, Maria Ascoli, Bruna, Zottis Poletti, Sílvia, Zier, Sandra S., Veiga, Vilmar, Franca da Cunha, Diego, Rucatti, Guilherme G., Igansi, Fernanda, Haeffner, Mauren P., Almeida, Viviane, Sanchez de Souza, Gabriela, Almeida, Mayana, dos Santos, Viviane, Oliveira, Natalia S., Edilena Paulino Azevedo, Bruna, Bizzaro Santos, Marco, Germann, Amanda, Gomes, Vitor, Homem, Rosa, Magedanz, Ellen, Laimer, Rosane, Tognon, Alexandre, Santos, Roberta P., Yumi Okada, Mariana, Paula Batista, Ana, Nogueira Rabaça, Aline, Miranda Trama, Larissa, Silva, Talita, de Souza Ormundo, Camila Thais, Vicente, Carla, Pinheiro, Caroline, Komar, Daniele, Walesiak, Olga, Malinowska, Katarzyna, Maksym, Jakub, Wojtera, Karolina, Fojt, Anna, Szczerba, Ewa, Swiderek, Marta, Wojtala, Ewelina, Karwowski, Jaroslaw, Łabyk, Andrzej, Szramowska, Agnieszka, Zdończyk, Olga, Jaroch, Joanna, Kolodziej, Adam, Marcinkiewicz-Siemion, Marta, Bockeria, Olga, Kudzoeva, Zalina, Aripova, Nodira, Naryshkin, Ivan A., Kuleshova, Alena, Malaev, Dastan, Subbotina, Irina, Gumerova, Victoria, Nikolaeva, Olga B., Fernández-Figares, Pharm, Virginia, Alonso-Álvarez, Moisés Blanco-Calvo Encarnación, García-González, Paula, Seijas Amigo, Jose, Fernández Martínez, Begoña Igual, Ana, Romero Aniorte, M. Quintana Giner A.I., Rivera Caravaca, J.M., Cañavate, Olga, Guerrero, Sonia, Riera, Silvia, Lasala, Maria, Lorenzo, Maria, Sobrino, Olga, Vazquez, Alexandra, Dong, Haojian, He, Peiyu, Xia, Chunli, Yang, Junqing, Zhong, Qi, Tian, Yanmeng, Li, Dongze, Li, Xiaomei, Ma, Xiang, Yu, Zixiang, Zhao, Qian, Li, Chunguang, Zhang, Lei, Zhao, Yu, Zhu, Bolin, Chen, Mulei, Chi, Hongjie, Wang, Yang, Zhang, Jing, Jing, Rui, Liu, Jingjing, Zhou, Qiang, Xu, Chang, Li, Zhuxi, Li, Junhua, Xiong, Luyang, Gao, Dan, Jiang, Dengke, Leng, Ran, Wang, Xutong, Yuan, Qianqian, Zhang, Lili, Bai, Ziliang, Li, Jianhua, Qi, Jie, Wang, Fei, Wang, Haitao, Yang, Bin, Yue, Zhou, Zhang, Zhulin, Dong, Yumei, Mao, Jiajia, Zhang, Bin, Li, Xiuhong, Yao, Xiaowei, Zhong, Nier, Zhou, Ning, Huang, Yaping, Zhou, Wei, Panpan, Peng, Yu Kunwu Yudong, Su, Xin, Wang, Chen, Zhao, Yunhai, Geng, Yaming, Wang, Yanfu, Fan, Jing-Yao, Feng, Si-Ting, Wang, Xiao, Yan, Yan, Zhang, Hui-Min, Chi, Lingping, Liu, Fang, Chen, Han, Jiang, Jun, Li, Huajun, Han, Yechen, Xu, Lihong, Chen, Gang, Hu, Rongrong, Pietrucci, Francesca, Di Donato, Anna, Pezzetta, Francesca, Casali, Valentina, Attanasio, Chiara, Leone, Gianpiero, Pisano, Francesco, Bare, Cristina, Fimiani, Fabio, Barioli, Alberto, Ramani, Federica, Rolfo, Fabrizio, Goletto, Cecilia, De Micco, Francesca, Di Marco, Stefano, Tricoli, Martina, Villella, Massimo, Tan, Sik-Yin V., Sia, Winnie C., Leong, Audrey W., Hai Yan, Li, Ismail, Nasrul, Tun Kyaw, Min, Yip, Deborah, Grahl, Dorit, Guenther, Franziska, Bonin, Kerstin, Wenzelburger, Ina, Gruensfelder, Susanne, Sinning, Jan-Malte, Weber, Marcel, Werner, Nikos, Steinmaurer, Gudrun, Winter, Tijana, Andric, Max-Paul, Tscharre, Claudia, Maximilian, Bernhard, Jäger, Wegmayrc, Egger, Floria, Davidovits, Judit Sebo Zoltan, Matics, Laszlone, Ágoston, Gergely, Dekany, Gabor, Bartykowszki, Andrea, Jakal, Agnes, Djokic, Jelena, Djordjevic-Dikic, Ana D., Giga, Vojislav L., Stepanovic, Jelena J., Velicki, Lazar, Pupic, Ljiljana, Simović, Stefan M., Stevo Martinovic, Miroslav, Stevanovic, Gordana, Dobric, Milan, Salinger Martinovic, Sonja, Stanojevic, Dragana, de Jesús-Pérez, Ramon, Brassetti, María Fernanda Canales, Adrián Vences Anaya, Diego, Pérez García, María, Estela Carvajal Juarez, Isabel, Madero Rovalo, Magdalena, Lee, Sau, Thomas, Prince, Chaplin, Melissa D., Stansborough, Jeanette K., Black, Marilyn, Bonner, Michelle M., Ireland, Kim F., Venn-Edmonds, Clare, Thobois, Corine, Tachot, Emilie, Laure, Christophe, Vassaliere, Christel, Abergel, Helene, Fuentes, Axelle, Eliahou, Ludivine, Dubourg, Olivier, Michaud, Pierre, Hadjih, Sarah, Brito, Patricia, Cornet, Charles, Rautureau, Jeremy, Juceviciene, Agne, Kalibataite-Rutkauskiene, Irma, Keinaite, Laura, Laukyte, Monika, Mikolaitiene, Gelmina, Smigelskaite, Akvile, Tamasauskiene, Ilona, Urboniene, Agne, Bouwhuis, Ilse, Nijmeijer, Jeannette, Lia, Elisabeth, J.M. Schoep, Ahoud, M. Janzen Sandra, Selas, Mafalda, Silva, Filipa, Freixo, Cláudia, Zimbarra Cabrita, Inês, Rocha, Andreia, Patuleia Figueiras, Francisca, Coelho, Andreia, Capinha, Marta, Inês Caetano, Maria, Silva, Susana, Tinnirello, Veronica, Nicolás Mungo, Matías, Garcia, Marina, Godoy, Valeria, Victoria Actis, Maria, Scaro, Graciela, Low, Liz, Scales, Jayne, Abercrombie, Kirsty, Howell, Leah, Patten, Cathrine, Björklund, Christina, Andreasson, Maria, Essermark, Marie, Persson, Liselotte, Harel, Or, Bentzvi, Margalit, Helmer, Ludmila, Ueda, Ikuko, Fujita, Jun, Furukawa, Akemi, Hirase, Kanae, Nagai, Toshiyuki, Otsuka, Fumiyuki, Nakano, Shintaro, Robesyn, Valerie, Yang, Yi-Hsuan, Mtana, Noloyiso, Anesini, Adriana, Maspoli, Simona, Mombelli, Manuela, Talaat, Ahmed, Rosca, Monica, Beladan, Carmen C., Zahrani, Sarah, Antonio Monsalve Davila, Marco, Khwakhong, Supatchara, Chaiyasri, Anong, Mekara, Warangkana, Kulthawong, Supap, Amaritakomol, Anong, Panpunuan, Pachara, Syamira Mokhtar, Noor, Asiah Basri, Nor, Yusnida, Irni, Hashim, Humayrah, Berger, Jeffrey, Williams, David, Harrington, Robert, Jiang, Lixin, Lopes, Renato D., Noel Bairey Merz, C., Weintraub, William, Donato Morales Rodríguez, Erick, Maurovich-Horvat, Pal, Sonawane, Poonam, Francis, Ramakrishnan, Rajesh, Nayak, T. Soundarya, Boer, Stephanie C., Rosenberg, Yves, Hamm, Christian, Helm, Malte, Peterson, Eric, Ballantyne, Christie, Calfas, Karen, Ann Champagne, Mary, Fleg, Jerome, McCullough, Peter A., Menasche, Philippe, Davidson, Michael, Fremes, Stephen, Guyton, Robert, Mack, Michael, Mohr, Fred, Rao, Anupama, Sabik, Joe, Shapira, Oz, Taggart, David, Tatoulis, James, Blankenship, Jim, Brener, Sorin, Buller, Chris, Colombo, Antonio, de Bruyne, Bernard, Kereiakes, Dean, Lefevre, Thierry, Moses, Jeffrey, Mahaffey, Ken, Cruz-Flores, Salvador, Danchin, Nicholas, Feen, Eli, Garcia, Mario J., Hauptman, Paul, Laddu, Abhay A., Passamani, Eugene, Pina, Ileana L., Simoons, Maarten, Skali, Hicham, Thygesen, Kristian, Waters, David, Endsley, Patricia, Esposito, Gerard, Kanters, Jeffrey, Pownall, John, Stournaras, Dimitrios, Friedrich, Matthias, Hachamovitch, Rory, Oliver, Dana, Harrel, Frank, Blume, Jeffrey, Lee, Kerry, Kullo, Iftikhar, McManus, Bruce, Newby, Kristin, Cohen, David, Bugiardini, Raffaele, Mattina, Deirdre, Ali, Ziad, Mathew, Roy, Friedman, Lawrence, Anderson, Jeffrey, Berg, Jessica, DeMets, David, Michael Gibson, C., Lamas, Gervasio, Deming, Nicole, Himmelfarb, Jonathan, Ouyang, Pamela, Woodard, Pamela, Nwosu, Samuel, Kirby, Ruth, Jeffries, Neal, Denaro, Jean E., Boumakis, Stephanie, Chan, Kevin, Cobb, Gia, Contreras, Aira, Cukali, Diana, Ferket, Stephanie, Gabriel, Andre, Hansen, Antonietta, Roberts, Arline, Chang, Michelle, Islam, Sharder, Wayser, Graceanne, Yakubov, Solomon, Yee, Michelle, Callison, Caroline, Hogan, Isabelle, Qelaj, Albertina, Pirro, Charlotte, Van Loo, Kerrie, Wisniewski, Brianna, Gilsenan, Margaret, Lang, Bevin, Mohamed, Samaa, Esquenazi-Karonika, Shari, Mathews, Patenne D., Naumova, Anna, Lyo, Jihyun, Setang, Vincent, Xavier, Mark, Anstrom, Kevin, Baloch, Khaula, Blount, Janet, Cowper, Patricia, Davidson-Ray, Linda, Drew, Laura, Harding, Tina, David Knight, J., Minshall Liu, Diane, O’Neal, Betsy, Redick, Thomas, Jones, Philip, Nugent, Karen, Jingyan Wang, Grace, Goyal, Abhinav, Hetrick, Holly, Hayes, Sean W., Friedman, John D., Mark Hyun, R. James Gerlach, Miranda-Peats, Romalisa, Slomka, Piotr, Thomson, Louise, Pierre Mongeon, Francois, Michael, Steven, Hung, Judy, Zeng, Xin, Eckstein, Jane, Guruge, Bandula, Streif, Mary, Alfonso, Maria A., Corral, Maria P., Garcia, Javier J., Horst, Jennifer, Jankovic, Ivana, Konigstein, Maayan, Lustre, Mitchel B., Peralta, Yolayfi, Sanchez, Raquel, Arsanjani, Reza, Elmor, Kimberly, Gomez, Millie, Hindoyan, Niree, Nakanishi, Rine, Barbara Srichai-Parsia, M., Yeoh, Eunice, Youn, Tricia, Bianchini, Francesca, Ceseri, Martina, Lorimer, Andrea, Magnoni, Marco, Orso, Francesco, Sarti, Laura, Mazza Barbosa, Lilian, Bello Duarte, Tauane, Colaiácovo Soares, Tamara, de Aveiro Morata, Julia, Carvalho, Pedro, de Carvalho Maffei, Natalia, Egydio, Flávia, Kawak, Anelise, Oliveira, Janaina, Restelli Piloto, Elissa, Pozzibon, Jaqueline, Camara, Diane, Mowafy, Neamat, Spindler, Caroline, Dai, Hao, Feng, Fang, Li, Jia, Li, Li, Liu, Jiamin, Xie, Qiulan, Zhang, Haibo, Zhang, Jianxin, Zhang, Lihua, Zhang, Liping, Zhang, Ning, Zhong, Hui, Escobar, Claudia, Eugenia Martin, Maria, Pascual, Andrea, Moraga, Paloma, Hernandez, Victoria, Posada, Maria, Fernandez, Sara, Luis Narro Villanueva, José, Selgas, Rafael, Luyten, Ann, Garcevic, Nevena, Stojkovic, Jelena, Ahmed, Asker, Bhatt, Richa, Chadha, Nitika, Kumar, Vijay, Lubna, Sadath, Naik, Pushpa, Pandey, Shruti, Ramasamy, Karthik, Saleem, Mohammed, Sharma, Pratiksha, and Siddaram, Hemalata

Published
2024
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22. Review of Implementation of ESG Norms in India

Author

Das, Rituparna, Das, Mononita Kundu, Roychoudhury, Saurav, Ghosh, Arijit, Chandan, Harish, Mitra, Nayan, Series Editor, Tanimoto, Kanji, Editorial Board Member, Schmidpeter, René, Series Editor, Idowu, Samuel O., Editorial Board Member, El-Bassiouny, Noha, Editorial Board Member, Chatterjee, Bhaskar, Editorial Board Member, Eweje, Gabriel, Editorial Board Member, Sharma, Tanuja, Editorial Board Member, Bhattacharya, Sonali, editor, Venkatesh, V. G., editor, and Chatterjee, Samir Ranjan, editor

Published
2024
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24. Colorful Helly Theorem for Piercing Boxes with Multiple Points

Author

Chakraborty, Sourav, Ghosh, Arijit, and Nandi, Soumi

Subjects
Computer Science - Computational Geometry, Mathematics - Combinatorics, 52A35
Abstract

Let $H_c=H_c(d,n)$ denote the smallest positive integer such that if we have a collection of families $\mathcal{F}_{1}, \dots, \mathcal{F}_{H_{c}}$ of axis-parallel boxes in $\mathbb{R}^{d}$ with the property that every colorful $H_{c}$-tuple from the above families can be pierced by $n$ points then there exits an $i\in \{ 1, \dots, H_{c}\}$, and for all $k\in \{ 1, \dots, H_{c}\} \setminus\{i\}$ there exists $F_k\in\mathcal{F}_k$ such that the following extended family $\mathcal{F}_i\cup\left\{F_k\;|\;k\in \{1, \dots, H_{c}\}\;\mbox{and} \;k\neq i\right\}$ can also be pierced by $n$ points. In this paper, we give a complete characterization of $H_{c}(d,n)$ for all values of $d$ and $n$. Our result is a colorful generalization of piercing axis-parallel boxes with multiple points by Danzer and Gr\"unbaum (Combinatorica 1982)., Comment: The manuscript has 19 pages and 3 figures. The title has been changed to better reflect the content of the paper. The abstract, introduction section, and Section 5 are new

Published
2022

25. Almost covering all the layers of hypercube with multiplicities

Author

Ghosh, Arijit, Kayal, Chandrima, and Nandi, Soumi

Subjects
Mathematics - Combinatorics, Computer Science - Discrete Mathematics, 05B40
Abstract

Given a hypercube $\mathcal{Q}^{n} := \{0,1\}^{n}$ in $\mathbb{R}^{n}$ and $k \in \{0, \dots, n\}$, the $k$-th layer $\mathcal{Q}^{n}_{k}$ of $\mathcal{Q}^{n}$ denotes the set of all points in $\mathcal{Q}^{n}$ whose coordinates contain exactly $k$ many ones. For a fixed $t \in \mathbb{N}$ and $k \in \{0, \dots, n\}$, let $P \in \mathbb{R}\left[x_{1}, \dots, x_{n}\right]$ be a polynomial that has zeroes of multiplicity at least $t$ at all points of $\mathcal{Q}^{n} \setminus \mathcal{Q}^{n}_{k}$, and $P$ has zeros of multiplicity exactly $t-1$ at all points of $\mathcal{Q}^{n}_{k}$. In this short note, we show that $$deg(P) \geq \max\left\{ k, n-k\right\}+2t-2.$$Matching the above lower bound we give an explicit construction of a family of hyperplanes $H_{1}, \dots, H_{m}$ in $\mathbb{R}^{n}$, where $m = \max\left\{ k, n-k\right\}+2t-2$, such that every point of $\mathcal{Q}^{n}_{k}$ will be covered exactly $t-1$ times, and every other point of $\mathcal{Q}^{n}$ will be covered at least $t$ times. Note that putting $k = 0$ and $t=1$, we recover the much celebrated covering result of Alon and F\"uredi (European Journal of Combinatorics, 1993). Using the above family of hyperplanes we disprove a conjecture of Venkitesh (The Electronic Journal of Combinatorics, 2022) on exactly covering symmetric subsets of hypercube $\mathcal{Q}^{n}$ with hyperplanes. To prove the above results we have introduced a new measure of complexity of a subset of the hypercube called index complexity which we believe will be of independent interest. We also study a new interesting variant of the restricted sumset problem motivated by the ideas behind the proof of the above result., Comment: 16 pages, substantial changes from previous version, title and abstract changed to better reflect the content of the paper

Published
2022
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26. Testing of Index-Invariant Properties in the Huge Object Model

Author

Chakraborty, Sourav, Fischer, Eldar, Ghosh, Arijit, Mishra, Gopinath, and Sen, Sayantan

Subjects
Computer Science - Data Structures and Algorithms, Mathematics - Statistics Theory
Abstract

The study of distribution testing has become ubiquitous in the area of property testing, both for its theoretical appeal, as well as for its applications in other fields of Computer Science. The original distribution testing model relies on samples drawn independently from the distribution to be tested. However, when testing distributions over the $n$-dimensional Hamming cube $\left\{0,1\right\}^{n}$ for a large $n$, even reading a few samples is infeasible. To address this, Goldreich and Ron [ITCS 2022] have defined a model called the huge object model, in which the samples may only be queried in a few places. In this work, we initiate a study of a general class of properties in the huge object model, those that are invariant under a permutation of the indices of the vectors in $\left\{0,1\right\}^{n}$, while still not being necessarily fully symmetric as per the definition used in traditional distribution testing. We prove that every index-invariant property satisfying a bounded VC-dimension restriction admits a property tester with a number of queries independent of n. To complement this result, we argue that satisfying only index-invariance or only a VC-dimension bound is insufficient to guarantee a tester whose query complexity is independent of n. Moreover, we prove that the dependency of sample and query complexities of our tester on the VC-dimension is tight. As a second part of this work, we address the question of the number of queries required for non-adaptive testing. We show that it can be at most quadratic in the number of queries required for an adaptive tester of index-invariant properties. This is in contrast with the tight exponential gap for general non-index-invariant properties. Finally, we provide an index-invariant property for which the quadratic gap between adaptive and non-adaptive query complexities for testing is almost tight., Comment: 66 pages, substantial changes from previous version, added new lower bound results (Theorem 1.4 and Theorem 1.7)

Published
2022

27. Tolerant Bipartiteness Testing in Dense Graphs

Author

Ghosh, Arijit, Mishra, Gopinath, Raychaudhury, Rahul, and Sen, Sayantan

Subjects
Computer Science - Data Structures and Algorithms
Abstract

Bipartite testing has been a central problem in the area of property testing since its inception in the seminal work of Goldreich, Goldwasser and Ron [FOCS'96 and JACM'98]. Though the non-tolerant version of bipartite testing has been extensively studied in the literature, the tolerant variant is not well understood. In this paper, we consider the following version of tolerant bipartite testing: Given a parameter $\varepsilon \in (0,1)$ and access to the adjacency matrix of a graph $G$, we can decide whether $G$ is $\varepsilon$-close to being bipartite or $G$ is at least $(2+\Omega(1))\varepsilon$-far from being bipartite, by performing $\widetilde{\mathcal{O}}\left(\frac{1}{\varepsilon ^3}\right)$ queries and in $2^{\widetilde{\mathcal{O}}(1/\varepsilon)}$ time. This improves upon the state-of-the-art query and time complexities of this problem of $\widetilde{\mathcal{O}}\left(\frac{1}{\varepsilon ^6}\right)$ and $2^{\widetilde{\mathcal{O}}(1/\varepsilon^2)}$, respectively, from the work of Alon, Fernandez de la Vega, Kannan and Karpinski (STOC'02 and JCSS'03), where $\widetilde{\mathcal{O}}(\cdot)$ hides a factor polynomial in $\log \frac{1}{\varepsilon}$., Comment: Accepted at ICALP'22. arXiv admin note: substantial text overlap with arXiv:2110.04574

Published
2022

30. Faster Counting and Sampling Algorithms using Colorful Decision Oracle

Author

Bhattacharya, Anup, Bishnu, Arijit, Ghosh, Arijit, and Mishra, Gopinath

Subjects
Computer Science - Data Structures and Algorithms
Abstract

In this work, we consider $d$-{\sc Hyperedge Estimation} and $d$-{\sc Hyperedge Sample} problem in a hypergraph $\mathcal{H}(U(\mathcal{H}),\mathcal{F}(\mathcal{H}))$ in the query complexity framework, where $U(\mathcal{H})$ denotes the set of vertices and $\mathcal{F}(\mathcal{H})$ denotes the set of hyperedges. The oracle access to the hypergraph is called {\sc Colorful Independence Oracle} ({\sc CID}), which takes $d$ (non-empty) pairwise disjoint subsets of vertices $A_1,\ldots,A_d \subseteq U(\mathcal{H})$ as input, and answers whether there exists a hyperedge in $\mathcal{H}$ having (exactly) one vertex in each $A_i, i \in \{1,2,\ldots,d\}$. The problem of $d$-{\sc Hyperedge Estimation} and $d$-{\sc Hyperedge Sample} with {\sc CID} oracle access is important in its own right as a combinatorial problem. Also, Dell {\it{et al.}}~[SODA '20] established that {\em decision} vs {\em counting} complexities of a number of combinatorial optimization problems can be abstracted out as $d$-{\sc Hyperedge Estimation} problems with a {\sc CID} oracle access. The main technical contribution of the paper is an algorithm that estimates $m= \lvert {\mathcal{F}(\mathcal{H})}\rvert$ with $\widehat{m}$ such that { $$ \frac{1}{C_{d}\log^{d-1} n} \;\leq\; \frac{\widehat{m}}{m} \;\leq\; C_{d} \log ^{d-1} n . $$ by using at most $C_{d}\log ^{d+2} n$ many {\sc CID} queries, where $n$ denotes the number of vertices in the hypergraph $\mathcal{H}$ and $C_{d}$ is a constant that depends only on $d$}. Our result coupled with the framework of Dell {\it{et al.}}~[SODA '21] implies improved bounds for a number of fundamental problems., Comment: To appear in STACS'2022, 22 pages

Published
2022

31. Uniform Brackets, Containers, and Combinatorial Macbeath Regions

Author

Dutta, Kunal, Ghosh, Arijit, and Moran, Shay

Subjects
Computer Science - Data Structures and Algorithms, Computer Science - Computational Complexity, Computer Science - Computational Geometry, Computer Science - Discrete Mathematics, Computer Science - Machine Learning, 68Q32 (Primary), 68Q11 (Secondary)
Abstract

We study the connections between three seemingly different combinatorial structures - "uniform" brackets in statistics and probability theory, "containers" in online and distributed learning theory, and "combinatorial Macbeath regions", or Mnets in discrete and computational geometry. We show that these three concepts are manifestations of a single combinatorial property that can be expressed under a unified framework along the lines of Vapnik-Chervonenkis type theory for uniform convergence. These new connections help us to bring tools from discrete and computational geometry to prove improved bounds for these objects. Our improved bounds help to get an optimal algorithm for distributed learning of halfspaces, an improved algorithm for the distributed convex set disjointness problem, and improved regret bounds for online algorithms against a smoothed adversary for a large class of semi-algebraic threshold functions., Comment: 21 pages. Full version of the ITCS'22 paper with the same title

Published
2021

33. Exploring the Gap between Tolerant and Non-tolerant Distribution Testing

Author

Chakraborty, Sourav, Fischer, Eldar, Ghosh, Arijit, Mishra, Gopinath, and Sen, Sayantan

Subjects
Computer Science - Data Structures and Algorithms
Abstract

The framework of distribution testing is currently ubiquitous in the field of property testing. In this model, the input is a probability distribution accessible via independently drawn samples from an oracle. The testing task is to distinguish a distribution that satisfies some property from a distribution that is far from satisfying it in the $\ell_1$ distance. The task of tolerant testing imposes a further restriction, that distributions close to satisfying the property are also accepted. This work focuses on the connection of the sample complexities of non-tolerant ("traditional") testing of distributions and tolerant testing thereof. When limiting our scope to label-invariant (symmetric) properties of distribution, we prove that the gap is at most quadratic. Conversely, the property of being the uniform distribution is indeed known to have an almost-quadratic gap. When moving to general, not necessarily label-invariant properties, the situation is more complicated, and we show some partial results. We show that if a property requires the distributions to be non-concentrated, then it cannot be non-tolerantly tested with $o(\sqrt{n})$ many samples, where $n$ denotes the universe size. Clearly, this implies at most a quadratic gap, because a distribution can be learned (and hence tolerantly tested against any property) using $\mathcal{O}(n)$ many samples. Being non-concentrated is a strong requirement on the property, as we also prove a close to linear lower bound against their tolerant tests. To provide evidence for other general cases (where the properties are not necessarily label-invariant), we show that if an input distribution is very concentrated, in the sense that it is mostly supported on a subset of size $s$ of the universe, then it can be learned using only $\mathcal{O}(s)$ many samples. The learning procedure adapts to the input, and works without knowing $s$ in advance., Comment: Added new results on constructive tolerant tester. Accepted at RANDOM 22

Published
2021

34. A Faster Algorithm for Max Cut in Dense Graphs

Author

Ghosh, Arijit, Mishra, Gopinath, Raychaudhury, Rahul, and Sen, Sayantan

Subjects
Computer Science - Data Structures and Algorithms
Abstract

We design an algorithm for approximating the size of \emph{Max Cut} in dense graphs. Given a proximity parameter $\varepsilon \in (0,1)$, our algorithm approximates the size of \emph{Max Cut} of a graph $G$ with $n$ vertices, within an additive error of $\varepsilon n^2$, with sample complexity $\mathcal{O}(\frac{1}{\varepsilon^3} \log^2 \frac{1}{\varepsilon} \log \log \frac{1}{\varepsilon})$ and query complexity of $\mathcal{O}(\frac{1}{\varepsilon^4} \log^3 \frac{1}{\varepsilon} \log \log \frac{1}{\varepsilon})$. Since Goldreich, Goldwasser and Ron (JACM 98) gave the first algorithm with sample complexity $\mathcal{O}(\frac{1}{\varepsilon^5}\log \frac{1}{\varepsilon})$ and query complexity of $\mathcal{O}(\frac{1}{\varepsilon^7}\log^2 \frac{1}{\varepsilon})$, there have been several efforts employing techniques from diverse areas with a focus on improving the sample and query complexities. Our work makes the first improvement in the sample complexity as well as query complexity after more than a decade from the previous best results of Alon, Vega, Kannan and Karpinski (JCSS 03) and of Mathieu and Schudy (SODA 08) respectively, both with sample complexity $\mathcal{O}\left(\frac{1}{{\varepsilon}^4}{\log}\frac{1}{\varepsilon}\right)$. We also want to note that the best time complexity of this problem was by Alon, Vega, Karpinski and Kannan (JCSS 03). By combining their result with an approximation technique by Arora, Karger and Karpinski (STOC 95), they obtained an algorithm with time complexity of $2^{\mathcal{O}(\frac{1}{{\varepsilon}^2} \log \frac{1}{\varepsilon})}$. In this work, we have improved this further to $2^{\mathcal{O}(\frac{1}{\varepsilon} \log \frac{1}{\varepsilon} )}$., Comment: The proof of the main claim in the paper is incomplete, and because of this reason, we are withdrawing the paper

Published
2021

35. On the Complexity of Triangle Counting using Emptiness Queries

Author

Bishnu, Arijit, Ghosh, Arijit, and Mishra, Gopinath

Subjects
Computer Science - Data Structures and Algorithms
Abstract

Beame et al. [ITCS 2018 & TALG 2021] introduced and used the Bipartite Independent Set (BIS) and Independent Set (IS) oracle access to an unknown, simple, unweighted and undirected graph and solved the edge estimation problem. The introduction of this oracle set forth a series of works in a short span of time that either solved open questions mentioned by Beame et al. or were generalizations of their work as in Dell and Lapinskas [STOC 2018], Dell, Lapinskas and Meeks [SODA 2020], Bhattacharya et al. [ISAAC 2019 & Theory Comput. Syst. 2021], and Chen et al. [SODA 2020]. Edge estimation using BIS can be done using polylogarithmic queries, while IS queries need sub-linear but more than polylogarithmic queries. Chen et al. improved Beame et al.'s upper bound result for edge estimation using IS and also showed an almost matching lower bound. Beame et al. in their introductory work asked a few open questions out of which one was on estimating structures of higher order than edges, like triangles and cliques, using BIS queries. In this work, we completely resolve the query complexity of estimating triangles using BIS oracle. While doing so, we prove a lower bound for an even stronger query oracle called Edge Emptiness (EE) oracle, recently introduced by Assadi, Chakrabarty and Khanna [ESA 2021] to test graph connectivity., Comment: 29 pages

Published
2021

38. Distance Estimation Between Unknown Matrices Using Sublinear Projections on Hamming Cube

Author

Bishnu, Arijit, Ghosh, Arijit, and Mishra, Gopinath

Subjects
Computer Science - Data Structures and Algorithms
Abstract

Using geometric techniques like projection and dimensionality reduction, we show that there exists a randomized sub-linear time algorithm that can estimate the Hamming distance between two matrices. Consider two matrices ${\bf A}$ and ${\bf B}$ of size $n \times n$ whose dimensions are known to the algorithm but the entries are not. The entries of the matrix are real numbers. The access to any matrix is through an oracle that computes the projection of a row (or a column) of the matrix on a vector in $\{0,1\}^n$. We call this query oracle to be an {\sc Inner Product} oracle (shortened as {\sc IP}). We show that our algorithm returns a $(1\pm \epsilon)$ approximation to ${{\bf D}}_{\bf M} ({\bf A},{\bf B})$ with high probability by making ${\cal O}\left(\frac{n}{\sqrt{{{\bf D}}_{\bf M} ({\bf A},{\bf B})}}\mbox{poly}\left(\log n, \frac{1}{\epsilon}\right)\right)$ oracle queries, where ${{\bf D}}_{\bf M} ({\bf A},{\bf B})$ denotes the Hamming distance (the number of corresponding entries in which ${\bf A}$ and ${\bf B}$ differ) between two matrices ${\bf A}$ and ${\bf B}$ of size $n \times n$. We also show a matching lower bound on the number of such {\sc IP} queries needed. Though our main result is on estimating ${{\bf D}}_{\bf M} ({\bf A},{\bf B})$ using {\sc IP}, we also compare our results with other query models., Comment: 30 pages. Accepted in RANDOM'21

Published
2021

39. Factors Associated With Coronary Angiography Performed Within 6 Months of Randomization to the Conservative Strategy in the ISCHEMIA Trial

Author

Pracoń, Radosław, Spertus, John A., Broderick, Samuel, Bangalore, Sripal, Rockhold, Frank W., Ruzyllo, Witold, Demchenko, Elena, Nageh, Thuraia, Grossman, Gabriel Blacher, Mavromatis, Kreton, Manjunath, Cholenahally N., Smanio, Paola E.P., Stone, Gregg W., Mancini, G.B. John, Boden, William E., Newman, Jonathan D., Reynolds, Harmony R., Hochman, Judith S., Maron, David J., Doan, John, Linefsky, Jason, Lee, Raven, Patel, Risha, Miller, Todd, Yang Cho, So, Milbrandt, Susan, Shelstad, Dawn, Banerjee, Subhash, Kamath, Preeti, Tejani, Ishita, Cobos, Stanley E., Quiles, Kirsten J., Dwyer, Raven R., Donnino, Robert M., Espinosa, Dalisa, Phillips, Lawrence M., Saric, Muhamed, Abdul-Nour, Khaled, Schley, Allison, Golden, Heather, Stone, Peter H., Osseni, Hermine, Wiyarand, Charlene, Douglass, Peter, Pomeroy, Hayley, Craft, Alexandra, Harvey, Bethany, Jang, James J., Anaya, Olivia, Yee, Gennie, Goold, Phoebe, Weitz, Steven, Giovannone, Steven, Pritchard, Lori, Arnold, Suzanne, Gans, Rosann, Henry O’Keefe, Jr, James, Kennedy, Paul, Shapiro, Michael D., Ganesan, Shobana, Schlichting, David, Naher, Aynun, El-Hajjar, Mohammad, Sidhu, Mandeep S., Fein, Steven A., Stewart, Wendy L., Torosoff, Mikhail T., Salmi, Kristin M., Lyubarova, Radmila, Mookherjee, Sulagna, Drzymalski, Krzysztof, McFalls, Edward O., Garcia, Santiago A., Bertog, Stefan C., Johnson, Debra K., Siddiqui, Rizwan A., Herrmann, Rebekah R., Ishani, Areef, Hansen, Ronnell A., Georges Khouri, Michel, Arges, Kristine, LeFevre, Melissa, Tomfohr, Jennifer, Goldberg, Jonathan L., Ann Byrne, Kimberly, Zappernick, Taissa, Goldweit, Richard, Canada, Sallie, Kakade, Meghana, Mieses, Patricia, Cobos, Stanley E., Dwyer, Raven R., Cohen, Ronny A., Espinosa, Dalisa, Mirrer, Brooks, Quiles, Kirsten J., Navarro, Victor, Rantinella, Magdalena, Rodriguez, Jessica, Mancilla, Olivia, Winchester, David E., Stinson, Susan, Kronenberg, Marvin, Weyand, Terry, Rogal, Philip, Crook, Sherron C., McFarren, Christopher, Heitner, John F., Ho, Jean, Khan, Saadat, Mohamed, Mahmoud, Dauber, Ira M., Soltau, Mary R., Rose, Delsa K., Wimmer, Rebecca J., Siegel, Kathy E., Derbyshire, Susan, Cannan, Charles, Dixon, Michelle, Leonard, Gerald, Sudarshan, Sriram, Heard, Ciarra, Gabriel, Viviana, Desire, Sukie, Mehta, Puja K., McDaniel, Michael, Rashid, Fauzia, Lerakis, Stamatios, Asier, Senait, Quyyumi, Arshed, Patel, Keyur, Wenger, Nanette K., Hedgepeth, Chester M., Gillis, Jennifer, Hurlburt, Heather, Manocchia, Megan, Rosen, Alan, Moore, Susan, Congdon, Elizabeth, Sahul, Zakir, Brandt, Gail, Marchelletta, Nora, Wippler, Kristina, Booth, David, Taul, Yvonne, Leung, Steve, Isaacs, Jennifer, Abdel-Latif, Ahmed, Bulkley, Viktoria, Reda, Hassan, Rodgers, Caroline, Ziada, Khaled, Setty, Sampoornima, Halverson, Kimberly E., Roraff, Christine, Thorsen, Jonean, Barua, Rajat S., Ojajuni, Amarachi, Olurinde, Oni, Surineni, Kamalakar, Hage, Fadi, Valaiyapathi, Badhma, Caldeira, Christiano, Davies, James E., Leesar, Massoud, Heo, Jaekyeong, Iskandrian, Amy, Al Solaiman, Firas, Singh, Satinder, Dajani, Khaled, Kartje, Carol M., El-Hajjar, Mohammad, Mesropian, Paul Der, Sacco, Joseph, Rawlins, Michele, McCandless, Brian, Thomson, Jennifer, Orgera, Marisa, Sidhu, Mandeep S., Colleen Rogge, Mary, Arif, Imran, Bunke, Julie, Kerr, Hanan, Unterbrink, Kendra, Fannon, Jacqueline, Burman, Cynthia, Trejo, Jorge F., Dubin, Marcia F., Fletcher, Gerald, Lane, Gary E., Neeson, Lynn M., Parikh, Pragnesh P., Pollak, Peter M., Shapiro, Brian P., Landolfo, Kevin, Gemignani, Anthony, Beaudry, Sarah, O’Rourke, Daniel, Meadows, Judith L., Tirado, Stephanie A., Halliday, Janet, Julian, Pamela, Call, Jason T., Lane, Stephanie M., Stanford, Jennifer L., Hannan, Joseph, Bojar, Robert, Arsenault, Patricia, Kumar, Deepti, Sigel, Pamela, Mukai, John, Martin, Edward T., Brooks, Miriam, Vorobiof, Gabriel, Douangvila, Ladda, Gevorgyan, Rubine, Moorman, Alec, Ranjbaran, Fatima, Smith, Bryn, Ohmart, Carly, Kinlay, Scott, Hamburger, Robert J., Rocco, Thomas P., Ly, Samantha, Bhatt, Deepak L., Quinn, Margot C., Croce, Kevin, Temiyasathit, Sara, Quin, Jacquelyn A, Do, Jacquelyn, Anumpa, Jati, Tobin, Desiree, Zenati, Marco, Faxon, David P, Rayos, Glenn, Langdon, Jennifer, Werner Bayer, Marcia, Seedhom, Ashraf, O’Malley, Amanda, Sullenberger, Lance, Orvis, Erin, Kumkumian, Gregory, Murphy, Mandy, Greenberg, Ann, Iraola, Margaret, Sedlis, Steven P., Maranan, Leandro C., Donnino, Robert M., Lorin, Jeffrey, Tamis-Holland, Jacqueline E., Malinay, Ammy, Kornberg, Robert, Leber, Robert, Saba, Souheil, Edillo, Candice P., Lee, Michael W., Small, Delano R., Nona, Wassim, Alexander, Patrick B., Rehman, Iram, Badami, Umesh, Ostrander, Ann, Wasmiller, Stephanie, Marzo, Kevin, Drewes, Wendy, Patel, Dipti, Robbins, Inga H., Levite, Howard A., White, Jackie M, Shetty, Sanjay, Hallam, Alison, Patel, Mayuri, Hamroff, Glenn S., Spooner, Benjamin J, Hollenweger, Linda M, Little, Raymond W., Little, Holly, Zimbelman, Brandi D., Little, Tiffany, Lui, Charles Y., Eskelson, Nona A, Smith, Brigham R., Vezina, Daniel P., Khor, Lillian L., Abraham, Josephine D., Bull, David A., McKellar, Stephen H., Booth, David, Taul, Yvonne, Kotter, John, Rodgers, Caroline, Abdel-Latif, Ahmed, Isaacs, Jennifer, Bulkley, Viktoria, Hu, Bob, Kaneshiro, Renee, Labovitz, Arthur J., Berlowitz, Michael, Kirby, Bonnie J., Rogal, Philip, Tran, Nhi N., McFarren, Christopher, Jahrsdorfer, Catherine, Matar, Fadi, Caldeira, Christiano, Rodriguez, Fatima, Yunis, Reem, Schnittger, Ingela, Patro, Jhina, Fearon, William F., Deedwania, Prakash, Vega, Antonia, Reddy, Kiran, Sweeny, Joseph, Bloise-Adames, Hugo, Jimenez, Santa, Saint Vrestil, Nicole, Bhandari, Reyna, Spizzieri, Christopher, Schade, Danielle, Yost, Roxanne, Hochberg, Claudia P, Beardsley, Paula, Fine, Denise, Salerno, William D., Tancredi, Jana, Arakelian, Patricia, Mathus, Susan, O’Neill, Deborah, Wyman, Ray, Burkhardt, Joy, Hosino, Suellen, Lubyanaya, Oksana A., Salas, Jose D., Zarka, Amer, Aguirre, Maria, Shah, Anil V., Dhawan, Manu, Parra, Diana, Tran, Tri, Haldis, Thomas, Weick, Catherine, Fowler-Lehman, Katie, Spitzer, Natalie, Riedberger, Casey, Weick, Catherine, Kohn, Jeffrey A., Cobos, Stanley E., Dwyer, Raven R., Espinosa, Dalisa, Quiles, Kirsten J., Girotra, Saket, Drum, Carrie, Miller-Cox, Kimberly, Ollinger, Amy, Almousalli, Omar, Capasso-Gulve, Elizabeth, Melanie Loehr, Alaine, Mosley, Marlowe, Krishnam, Mayil S., Heydari, Shirin, Milliken, Jeffrey C., Lundeen, Andrea M., Patel, Pranav M., Karanjah, Edgar, Seto, Arnold H., Marfori, Wanda C., Harley, Kevin T., Hernandez-Rangel, Eduardo, Gibson, Michael A., Singh, Pam, Allen, Byron J., Coram, Rita, Marie Webb, Anne, Fridell, Ellie, Wilson, Heidi, Thomas, Sabu, Kim, Angela, Schwartz, Ronald G, Wilmot, Patrick, Chen, Wei, El Shahawy, Mahfouz, Stevens, Ramona, Stafford, James, Black, Loriane, Abernethy, William B., Hull, Amber B., Lim, Olivia J., Tucker, Helen C., Putnam, Natasha C., Hall, Linda L., Cauthren, Tia, Tucker, Trish, Zurick, Andrew, Horton, Hollie, Orga, Jan, Meyer, Thomas M., White, Joyce R., Morford, Ronald G., Baumann, Cynthia, Rutkin, Bruce, Seeratan, Vidya, Bokhari, Sabahat, Jimenez, Magnolia, Sokol, Seth I., Schultz, Cidney, Meisner, Jay, Russo, Jeanne, Hamzeh, Ihab, Misra, Arunima, Huda, Zohra, Wall, Matthew, Boan, Araceli, Lenges De Rosen, Veronica, Alam, Mahboob, Turner, Michael C., Hinton, Christine R, Mulhearn, Thomas J., Good, Arnold P., Archer, Beth A., Dionne, Julia S., Allardyce, Cheryl A., Sikora, Lindsey N., Czerniak, Jennifer H., Mull, Jennifer A., Ferguson, Elizabeth, Laube, Frances, Shammas, Nicolas W., Shammas, Gail A, Christensen, Lori, Park, Holly, Chilton, Robert, Hecht, Joan, Nguyen, Patricia K., Vo, Davis, Hirsch, James, Jezior, Matthew, Bindeman, Jody, Salkind, Sara, Espinosa, Dalisa, Desimone, Lori-Ann, Gordon, Paul C., Felix-Stern, Lina, Crain, Thomas, Gomes, Jassira, Gordon, Catherine, Stenberg, Robert, Mann, Aimee, McCreary, Theresa, Pedalino, Ronald P., Cobos, Stanley E., Dwyer, Raven R., Espinosa, Dalisa, Quiles, Kirsten J., Wiesel, Joseph, Cobos, Stanley E., Dwyer, Raven R., Espinosa, Dalisa, Quiles, Kirsten J., Juang, George J., Gopaul, Candace, Hultberg, Karen, Huk, Tauqir, Hussain, Afshan, Al-Amoodi, Mohammed, Zambrano, Yesenia, Medina Rodriguez, Sarah, Milner, Trudie, Wohns, David, Mulder, Abbey, Van Oosterhout, Stacie, Lader, Ellis W., Meyer, Martha, Mumma, Michael, Clapp, Nancy L., Barrentine, Heather, Dharmarajan, Lekshmi, Jose, Jenne M., Cobos, Stanley E., Dwyer, Raven R., Espinosa, Dalisa, Quiles, Kirsten J., Manchery, Jenne, McGarvey Jr, Joseph F.X., McKinney, Vera, Schwarz, Linda, Downes, Thomas R., Kaczkowski, Scott M., Luckasen, Gary J., Jaskowiak, Adam J., Klitch, Joel, Cheong, Benjamin, Dees, Debra, Potluri, Srinivasa, Vasquez, Precilia, Mastouri, Ronald A., Breall, Jeffery A., Hannemann, Elise L., Revtyak, George E., Mae Foltz, Judy, Bazeley, Jonathan W., Li, Dayuan, DeRosa, Emily, Jorgenson, Beth, Riestenberg-Smith, Joyce, Giedd, Kenneth, Old, Wayne, Bariciano, Rebecca, Burt, Francis, Sokhon, Kozhaya, Waldron, Jessica, Mayon, Michelle, Gopal, Deepika, Valeti, Uma S., Ann Peichel, Gretchen, Kobashigawa, Jon, Starks, Brandy, Garcia, Lucilla, Thottam, Maria, Bhargava, Balram, Anand, Anjali, Chakanalil Govindan, Sajeev, Raj, Janitha, Gopalan Nair, Rajesh, Ravindran, Reshma, Rajalekshmi, VS, Nataraj, Nandita, Moorthy, Nagaraja, Nayak, Soundarya, Mylarappa, Mahevamma, Narayanappa, Suryaprakash, Pandit, Neeraj, Bajaj, Sheromani, Kumar Nath, Ranjit, Yadav, Vandana, Mishra, Girish, Dwivedi, S.K., Tewari, Roma, Narain, V.S., Mishra, Meenakshi, Chandra, Sharad, Patel, Shivali, Singh, Suman, Wander, Gurpreet S., Tandon, Rohit, Ralhan, Sarju, Kaur, Baljeet, Aslam, Naved, Gupta, Sonika, Goyal, Abhishek, Bhargava, Balram, Suvarna, Chandini, Karthikeyan, G., Ramakrishnan, S., Seth, Sandeep, Yadav, Rakesh, Singh, Sandeep, Roy, Ambuj, Parakh, Neeraj, Kumar Verma, Sunil, Narang, Rajiv, Mishra, Sundeep, Naik, Nitish, Sharma, Gautam, Kumar Choudhary, Shiv, Patel, Chetan, Gulati, Gurpreet, Sharma, Sanjeev, Bahl, V K, Mathew, Anoop, Mannekkattukudy Kurian, Binoy, Punnoose, Eapen, Avdhoot Gadkari, Milind, Rupesh Karwa, Sheetal, Gadage, Siddharth, Kolhe, Suvarna, Umesh Pillay, Tapan, Satheesh, Santhosh, Vindhya, R. 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G., Wright, Judith, Exley, Donna, Sirker, Alexander A, Andiapen, Mervyn, Richards, Amy J., Hoole, Stephen P, Wong, Lisa, Witherow, Fraser N., Munro, Melanie J., Johnston, Nicola, Harbinson, Mark, McEvoy, Michelle, Walsh, Simon, Brown, Caroline, Douglas, Hanna, Luckie, Matthew, Charles, Thabitha, Kolakaluri, Laurel, Phillips, Hannah, Sobolewska, Jolanta, Morby, Louise, Hallett, Karen, Corbett, Carolyn, Winstanley, Lynne, Jeetley, Paramjit, Smit, Angelique, Patel, Niket, Kotecha, Tushar, Travill, Christopher, Gent, Susan, Karimullah, Iqbal, Hussain, Nafisa, Al-Bustami, Mahmud, Braganza, Denise, Haines, Fiona, Taaffe, Joanne, Henderson, Robert, Burton, Jane, Pointon, Kate, Colton, Maria, Naik, Surendra, King, Rachel, Mathew, Thomas, Brown, Ammani, Docherty, Andrew, Berry, Colin, McCloy, Lisa, Collison, Damien, Robb, Kate, Roditi, Giles, Paterson, Craig, Crawford, Wenda, Kelly, Joanne, McGregor, Lorraine, Moriarty, Andrew J, Mackin, Anne, Glover, Jason D., Knight, Janet P, Pradhan, Jiwan, Mikhail, Ghada, Bose, Tuhina, Francis, Darrel P., Dzavik, Vladimir, Goodman, Shaun, Gosselin, Gilbert, Gosselin, Gilbert, Proietti, Anna, Brousseau, Myriam, Corfias, Magalie, Blaise, Patricia, Harvey, Luc, Diaz, Ariel, Rheault, Philippe, Barrero, Miguel, Gagné, Carl-Éric, Alarie, Patricia, Pépin-Dubois, Yanek, Arcand, Linda, Costa, Ricardo, Roy, Isabelle, Tung Sia, Ying, Montpetit, Estelle, Lemay, Catherine, Gisbert, Alejandro, Gervais, Pierre, Rheault, Alain, Drouin, Katia, Carl Phaneuf, Denis, Bergeron, Christine, Gosselin, Gilbert, Shelley, Christine, Masson, Christine, Garg, Pallav, Carr, Sandy, Bone, Catherine, Chow, Benjamin J.W., Moga, Ermina, Hessian, Renee C., Kourzenkova, Janetta, Beanlands, Rob S., Walter, Olga, Davies, Richard F., Bainey, Kevin R., Hogg, Norma, Welsh, Suzanne, Cheema, Asim N., Bagai, Akshay, Wald, Ron, Goodman, Shaun, Kushniriuk, Khrystyna, Joseph Graham, John, Hussain, Mohammed, Peterson, Mark, Bello, Olugbenga, Chow, Chi-Ming, Abramson, Beth, Nazir Cheema, Asim, Syed, Ishba, Hussain, Mohammed, Kushniriuk, Khrystyna, Cha, James, Otis, Judy, Otis, Rebecca, Howarth, Andrew G, Seib, Michelle M, Rivest, Sandra M, Sandonato, Rosa, Wong, Graham, Chow, Jackie, Starovoytov, Andrew, Uchida, Naomi, Meadows, Ngaire, Uxa, Amar, Asif, Nadia, Tavares, Suzana, Galiwango, Paul, Bozek, Bev, Kassam, Saleem, Shier, Maria, Mukherjee, Ashok, Larmand, Lori-Ann, Ricci, A. 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Published
2024
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41. Query Complexity of Global Minimum Cut

Author

Bishnu, Arijit, Ghosh, Arijit, Mishra, Gopinath, and Paraashar, Manaswi

Subjects
Computer Science - Data Structures and Algorithms
Abstract

In this work, we resolve the query complexity of global minimum cut problem for a graph by designing a randomized algorithm for approximating the size of minimum cut in a graph, where the graph can be accessed through local queries like {\sc Degree}, {\sc Neighbor}, and {\sc Adjacency} queries. Given $\epsilon \in (0,1)$, the algorithm with high probability outputs an estimate $\hat{t}$ satisfying the following $(1-\epsilon) t \leq \hat{t} \leq (1+\epsilon) t$, where $m$ is the number of edges in the graph and $t$ is the size of minimum cut in the graph. The expected number of local queries used by our algorithm is $\min\left\{m+n,\frac{m}{t}\right\}\mbox{poly}\left(\log n,\frac{1}{\epsilon}\right)$ where $n$ is the number of vertices in the graph. Eden and Rosenbaum showed that $\Omega(m/t)$ many local queries are required for approximating the size of minimum cut in graphs. These two results together resolve the query complexity of the problem of estimating the size of minimum cut in graphs using local queries. Building on the lower bound of Eden and Rosenbaum, we show that, for all $t \in \mathbb{N}$, $\Omega(m)$ local queries are required to decide if the size of the minimum cut in the graph is $t$ or $t-2$. Also, we show that, for any $t \in \mathbb{N}$, $\Omega(m)$ local queries are required to find all the minimum cut edges even if it is promised that the input graph has a minimum cut of size $t$. Both of our lower bound results are randomized, and hold even if we can make {\sc Random Edge} query apart from local queries., Comment: 15 pages

Published
2020

42. Disjointness through the Lens of Vapnik-Chervonenkis Dimension: Sparsity and Beyond

Author

Bhattacharya, Anup, Chakraborty, Sourav, Ghosh, Arijit, Mishra, Gopinath, and Paraashar, Manaswi

Subjects
Computer Science - Computational Complexity, Computer Science - Computational Geometry
Abstract

The disjointness problem - where Alice and Bob are given two subsets of $\{1, \dots, n\}$ and they have to check if their sets intersect - is a central problem in the world of communication complexity. While both deterministic and randomized communication complexities for this problem are known to be $\Theta(n)$, it is also known that if the sets are assumed to be drawn from some restricted set systems then the communication complexity can be much lower. In this work, we explore how communication complexity measures change with respect to the complexity of the underlying set system. The complexity measure for the set system that we use in this work is the Vapnik-Chervonenkis (VC) dimension. More precisely, on any set system with VC dimension bounded by $d$, we analyze how large can the deterministic and randomized communication complexities be, as a function of $d$ and $n$. In this paper, we construct two natural set systems of VC dimension $d$, motivated from geometry. Using these set systems we show that the deterministic and randomized communication complexity can be $\widetilde{\Theta}\left(d\log \left( n/d \right)\right)$ for set systems of VC dimension $d$ and this matches the deterministic upper bound for all set systems of VC dimension $d$. We also study the deterministic and randomized communication complexities of the set intersection problem when sets belong to a set system of bounded VC dimension. We show that there exists set systems of VC dimension $d$ such that both deterministic and randomized (one-way and multi-round) complexity for the set intersection problem can be as high as $\Theta\left( d\log \left( n/d \right) \right)$, and this is tight among all set systems of VC dimension $d$., Comment: To appear in RANDOM 2020. Pages: 15

Published
2020

44. Analysis of One-Dimensional 4-State Cellular Automata Rules and DNA Evolutions

Author

Ghosh, Arijit, Behera, Suchitra, Padhi, Sagarika, Sahoo, Sudhakar, Kacprzyk, Janusz, Series Editor, Pal, Nikhil R., Advisory Editor, Bello Perez, Rafael, Advisory Editor, Corchado, Emilio S., Advisory Editor, Hagras, Hani, Advisory Editor, Kóczy, László T., Advisory Editor, Kreinovich, Vladik, Advisory Editor, Lin, Chin-Teng, Advisory Editor, Lu, Jie, Advisory Editor, Melin, Patricia, Advisory Editor, Nedjah, Nadia, Advisory Editor, Nguyen, Ngoc Thanh, Advisory Editor, Wang, Jun, Advisory Editor, Das, Sukanta, editor, and Martinez, Genaro Juarez, editor

Published
2023
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