275 research outputs found
Block Rigidity: Strong Multiplayer Parallel Repetition Implies Super-Linear Lower Bounds for Turing Machines
We prove that a sufficiently strong parallel repetition theorem for a special
case of multiplayer (multiprover) games implies super-linear lower bounds for
multi-tape Turing machines with advice. To the best of our knowledge, this is
the first connection between parallel repetition and lower bounds for time
complexity and the first major potential implication of a parallel repetition
theorem with more than two players.
Along the way to proving this result, we define and initiate a study of block
rigidity, a weakening of Valiant's notion of rigidity. While rigidity was
originally defined for matrices, or, equivalently, for (multi-output) linear
functions, we extend and study both rigidity and block rigidity for general
(multi-output) functions. Using techniques of Paul, Pippenger, Szemer\'edi and
Trotter, we show that a block-rigid function cannot be computed by multi-tape
Turing machines that run in linear (or slightly super-linear) time, even in the
non-uniform setting, where the machine gets an arbitrary advice tape.
We then describe a class of multiplayer games, such that, a sufficiently
strong parallel repetition theorem for that class of games implies an explicit
block-rigid function. The games in that class have the following property that
may be of independent interest: for every random string for the verifier
(which, in particular, determines the vector of queries to the players), there
is a unique correct answer for each of the players, and the verifier accepts if
and only if all answers are correct. We refer to such games as independent
games. The theorem that we need is that parallel repetition reduces the value
of games in this class from to , where is the number of
repetitions.
As another application of block rigidity, we show conditional size-depth
tradeoffs for boolean circuits, where the gates compute arbitrary functions
over large sets.Comment: 17 pages, ITCS 202
Polynomial Bounds On Parallel Repetition For All 3-Player Games With Binary Inputs
We prove that for every 3-player (3-prover) game with value less
than one, whose query distribution has the support of hamming weight one vectors, the value of the -fold
parallel repetition decays polynomially fast to zero;
that is, there is a constant such that the value of the
game is at most .
Following the recent work of Girish, Holmgren, Mittal, Raz and Zhan (STOC
2022), our result is the missing piece that implies a similar bound for a much
more general class of multiplayer games: For 3-player game
over and , with value less than 1, there is a constant
such that the value of the game is at most .
Our proof technique is new and requires many new ideas. For example, we make
use of the Level- inequalities from Boolean Fourier Analysis, which, to the
best of our knowledge, have not been explored in this context prior to our
work
Polynomial Bounds on Parallel Repetition for All 3-Player Games with Binary Inputs
We prove that for every 3-player (3-prover) game G with value less than one, whose query distribution has the support S = {(1,0,0), (0,1,0), (0,0,1)} of Hamming weight one vectors, the value of the n-fold parallel repetition G^{?n} decays polynomially fast to zero; that is, there is a constant c = c(G) > 0 such that the value of the game G^{?n} is at most n^{-c}.
Following the recent work of Girish, Holmgren, Mittal, Raz and Zhan (STOC 2022), our result is the missing piece that implies a similar bound for a much more general class of multiplayer games: For every 3-player game G over binary questions and arbitrary answer lengths, with value less than 1, there is a constant c = c(G) > 0 such that the value of the game G^{?n} is at most n^{-c}.
Our proof technique is new and requires many new ideas. For example, we make use of the Level-k inequalities from Boolean Fourier Analysis, which, to the best of our knowledge, have not been explored in this context prior to our work
Parallel Repetition for the GHZ Game: A Simpler Proof
We give a new proof of the fact that the parallel repetition of the (3-player) GHZ game reduces the value of the game to zero polynomially quickly. That is, we show that the value of the n-fold GHZ game is at most n^{-?(1)}. This was first established by Holmgren and Raz [Holmgren and Raz, 2020]. We present a new proof of this theorem that we believe to be simpler and more direct. Unlike most previous works on parallel repetition, our proof makes no use of information theory, and relies on the use of Fourier analysis.
The GHZ game [Greenberger et al., 1989] has played a foundational role in the understanding of quantum information theory, due in part to the fact that quantum strategies can win the GHZ game with probability 1. It is possible that improved parallel repetition bounds may find applications in this setting.
Recently, Dinur, Harsha, Venkat, and Yuen [Dinur et al., 2017] highlighted the GHZ game as a simple three-player game, which is in some sense maximally far from the class of multi-player games whose behavior under parallel repetition is well understood. Dinur et al. conjectured that parallel repetition decreases the value of the GHZ game exponentially quickly, and speculated that progress on proving this would shed light on parallel repetition for general multi-player (multi-prover) games
Poland syndrome, a rare congenital disorder with no functional deficit: a case report
Poland syndrome is a rare congenital syndrome. Most of the reported cases are sporadic, pattern of genetic inheritance is not known. It is an anomaly in which there is underdeveloped or absent pectoralis major and minor muscles leading to abnormal appearance of chest on the involved side. Most cases are unilateral with minimal functional abnormality in majority of the cases but with major cosmetic concerns for the patient. Surgery is rarely indicated but if required is done mainly for cosmetic purposes. We report a case of Poland syndrome in a young healthy individual as it started becoming evident
Multi-modal Extreme Classification
This paper develops the MUFIN technique for extreme classification (XC) tasks
with millions of labels where datapoints and labels are endowed with visual and
textual descriptors. Applications of MUFIN to product-to-product recommendation
and bid query prediction over several millions of products are presented.
Contemporary multi-modal methods frequently rely on purely embedding-based
methods. On the other hand, XC methods utilize classifier architectures to
offer superior accuracies than embedding only methods but mostly focus on
text-based categorization tasks. MUFIN bridges this gap by reformulating
multi-modal categorization as an XC problem with several millions of labels.
This presents the twin challenges of developing multi-modal architectures that
can offer embeddings sufficiently expressive to allow accurate categorization
over millions of labels; and training and inference routines that scale
logarithmically in the number of labels. MUFIN develops an architecture based
on cross-modal attention and trains it in a modular fashion using pre-training
and positive and negative mining. A novel product-to-product recommendation
dataset MM-AmazonTitles-300K containing over 300K products was curated from
publicly available amazon.com listings with each product endowed with a title
and multiple images. On the all datasets MUFIN offered at least 3% higher
accuracy than leading text-based, image-based and multi-modal techniques. Code
for MUFIN is available at https://github.com/Extreme-classification/MUFI
An Analytical Study of Rumoured Tweets by Using Twitter Data
Earlier when the internet was not there, rumours were spread by word of mouth technique but in this era of technology where we have social networking sites like twitter, rumours can be spread easily and quickly and a situation of panic can arise. Twitter is an American online news and social networking service on which users finds the latest news and world events faster. It is used for communication, interaction withpeople, announcement of event etc. from breaking news to sports, politics and everyday interests, one can find this service very addictive and an easy way to gather information about a certain event. Businesses can also use it to build their own brands and for marketing. But the founders of twitter like jack Dorsey forgot one thing that every coin has two sides. While twitter is a great way to interact with the masses, it is also a home of spammers. Spamming is a very common thing on twitter. Spammers create twitter accounts to perform a variety of tasks like posting links with unrelated tweets and the speed at which these fake and malicious misinformation spread on twitter in a real-time emergencies always causing a huge flood of tweets on twitter. In this paper, we demonstrated an analytical study of those rumoured tweets by twitter data. Using some of the rumoured tweets posted during the Chennai flood in 2015 and some non-rumoured tweets, we trained a classifier. The ability to track rumours and predict their outcomes have many applications for journalists, emergency services, and thereforehelp in minimizing the impact of false and fake information on this twitter platform
Molecular dynamics simulations of glassy polymers
We review recent results from computer simulation studies of polymer glasses,
from chain dynamics around the glass transition temperature Tg to the
mechanical behaviour below Tg. These results clearly show that modern computer
simulations are able to address and give clear answers to some important issues
in the field, in spite of the obvious limitations in terms of length and time
scales. In the present review we discuss the cooling rate effects, and dynamic
slowing down of different relaxation processes when approaching Tg for both
model and chemistry-specific polymer glasses. The impact of geometric
confinement on the glass transition is discussed in detail. We also show that
computer simulations are very useful tools to study structure and mechanical
response of glassy polymers. The influence of large deformations on mechanical
behaviour of polymer glasses in general, and strain hardening effect in
particular are reviewed. Finally, we suggest some directions for future
research, which we believe will be soon within the capabilities of state of the
art computer simulations, and correspond to problems of fundamental interest.Comment: To apear in "Soft Matter
Quantum-centric Supercomputing for Materials Science: A Perspective on Challenges and Future Directions
Computational models are an essential tool for the design, characterization,
and discovery of novel materials. Hard computational tasks in materials science
stretch the limits of existing high-performance supercomputing centers,
consuming much of their simulation, analysis, and data resources. Quantum
computing, on the other hand, is an emerging technology with the potential to
accelerate many of the computational tasks needed for materials science. In
order to do that, the quantum technology must interact with conventional
high-performance computing in several ways: approximate results validation,
identification of hard problems, and synergies in quantum-centric
supercomputing. In this paper, we provide a perspective on how quantum-centric
supercomputing can help address critical computational problems in materials
science, the challenges to face in order to solve representative use cases, and
new suggested directions.Comment: 60 pages, 14 figures; comments welcom
Optimasi Portofolio Resiko Menggunakan Model Markowitz MVO Dikaitkan dengan Keterbatasan Manusia dalam Memprediksi Masa Depan dalam Perspektif Al-Qur`an
Risk portfolio on modern finance has become increasingly technical, requiring the use of sophisticated mathematical tools in both research and practice. Since companies cannot insure themselves completely against risk, as human incompetence in predicting the future precisely that written in Al-Quran surah Luqman verse 34, they have to manage it to yield an optimal portfolio. The objective here is to minimize the variance among all portfolios, or alternatively, to maximize expected return among all portfolios that has at least a certain expected return. Furthermore, this study focuses on optimizing risk portfolio so called Markowitz MVO (Mean-Variance Optimization). Some theoretical frameworks for analysis are arithmetic mean, geometric mean, variance, covariance, linear programming, and quadratic programming. Moreover, finding a minimum variance portfolio produces a convex quadratic programming, that is minimizing the objective function ðð¥with constraintsð ð 𥠥 ðandð´ð¥ = ð. The outcome of this research is the solution of optimal risk portofolio in some investments that could be finished smoothly using MATLAB R2007b software together with its graphic analysis
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