Related papers: Conditional Expectation Bounds with Applications i…
Many key quantities in statistics and probability theory such as the expectation, quantiles, expectiles and many risk measures are law-determined maps from a space of random variables to the reals. We call such a law-determined map, which…
In order to be practically useful, quantum cryptography must not only provide a guarantee of secrecy, but it must provide this guarantee with a useful, sufficiently large throughput value. The standard result of generalized privacy…
We prove that a formula predicted on the basis of non-rigorous physics arguments [Zdeborova and Krzakala: Phys. Rev. E (2007)] provides a lower bound on the chromatic number of sparse random graphs. The proof is based on the interpolation…
The goal of this paper is to introduce ideas and methodology of the generic case complexity to cryptography community. This relatively new approach allows one to analyze the behavior of an algorithm on ''most'' inputs in a simple and…
This paper investigates and bounds the expected solution quality of combinatorial optimization problems when feasible solutions are chosen at random. Loose general bounds are discovered, as well as families of combinatorial optimization…
Expectiles are statistical parameters which also provide a class of sublinear risk measures in finance. They are solutions of continuous optimization problems. The corresponding first order condition provides two different fixed point…
In this note, we formulate a "one-sided" version of Wormald's differential equation method. In the standard "two-sided" method, one is given a family of random variables which evolve over time and which satisfy some conditions including a…
We discuss some properties of conditional expectation operators, and use these facts to prove an interesting counterexample regarding sufficient statistics. In particular, we show that there exists sufficient random variables X and Y, such…
An approach to reasoning with default rules where the proportion of exceptions, or more generally the probability of encountering an exception, can be at least roughly assessed is presented. It is based on local uncertainty propagation…
Theoretically, the conditional expectation of a square-integrable random variable $Y$ given a $d$-dimensional random vector $X$ can be obtained by minimizing the mean squared distance between $Y$ and $f(X)$ over all Borel measurable…
In recent years, the analysis of a control barrier function has received considerable attention because it is helpful for the safety-critical control required in many control application problems. While the extension of the analysis to a…
The Chernoff bound is one of the most widely used tools in theoretical computer science. It's rare to find a randomized algorithm that doesn't employ a Chernoff bound in its analysis. The standard proofs of Chernoff bounds are beautiful but…
One-sided output secure function evaluation is a cryptographic primitive where the two mutually distrustful players, Alice and Bob, both have a private input to a bivariate function. Bob obtains the value of the function for the given…
For a linear combination of random variables, fix some confidence level and consider the quantile of the combination at this level. We are interested in the partial derivatives of the quantile with respect to the weights of the random…
We consider the classical coupled, combined-field integral equation formulations for time-harmonic acoustic scattering by a sound soft bounded obstacle. In recent work, we have proved lower and upper bounds on the $L^2$ condition numbers…
Modern authentication systems store hashed values of passwords of users using cryptographic hash functions. Therefore, to crack a password an attacker needs to guess a hash function input that is mapped to the hashed value, as opposed to…
The need to condition distributional properties such as expectation, variance, and entropy arises in algorithmic fairness, model simplification, robustness and many other areas. At face value however, distributional properties are not…
Shape estimation and object reconstruction are common problems in image analysis. Mathematically, viewing objects in the image plane as random sets reduces the problem of shape estimation to inference about sets. Currently existing…
We obtain expected number of arrivals, absorption probabilities and expected time until absorption for an asymmetric discrete random walk on a graph in the presence of multiple function barriers. On each edge of the graph and in each vertex…
Weak pseudorandom functions (wPRFs) found an important application as main building blocks for leakage-resilient ciphers (EUROCRYPT'09). Several security bounds, based on different techniques, were given to these stream ciphers. The…