Related papers: Negatively Reinforced Balanced Urn Schemes
Multivariable Mendelian randomization (MVMR) uses genetic variants as instrumental variables to infer the direct effects of multiple exposures on an outcome. However, unlike univariable Mendelian randomization, MVMR often faces greater…
Most studies for postselected weak measurement in optomechanical system focus on using a single photon as a measured system. However, we find that using weak coherent light instead of a single photon can also amplify the mirror's position…
A cyclic urn is an urn model for balls of types $0,\ldots,m-1$. The urn starts at time zero with an initial configuration. Then, in each time step, first a ball is drawn from the urn uniformly and independently from the past. If its type is…
Human recursive numeral systems (i.e., counting systems such as English base-10 numerals), like many other grammatical systems, are highly regular. Following prior work that relates cross-linguistic tendencies to biases in learning, we ask…
We present an alternative voting system that aims at bridging the gap between proportional representative systems and majoritarian, single winner election systems. The system lets people vote for multiple parties, but then assigns each…
While it is well known that a Turing machine equipped with the ability to flip a fair coin cannot compute more that a standard Turing machine, we show that this is not true for a biased coin. Indeed, any oracle set $X$ may be coded as a…
When making causal inferences, post-treatment confounders complicate analyses of time-varying treatment effects. Conditioning on these variables naively to estimate marginal effects may inappropriately block causal pathways and may induce…
In model-free deep reinforcement learning (RL) algorithms, using noisy value estimates to supervise policy evaluation and optimization is detrimental to the sample efficiency. As this noise is heteroscedastic, its effects can be mitigated…
We study kernel quadrature rules with convex weights. Our approach combines the spectral properties of the kernel with recombination results about point measures. This results in effective algorithms that construct convex quadrature rules…
The reachability analysis of weighted pushdown systems is a very powerful technique in verification and analysis of recursive programs. Each transition rule of a weighted pushdown system is associated with an element of a bounded semiring…
This paper studies the allocation of voting weights in a committee representing groups of different sizes. We introduce a partial ordering of weight allocations based on stochastic comparison of social welfare. We show that when the number…
Among other things, we prove that, for a doubling weight $w$, $0< p\leq\infty$, $r\in{\mathbb N}_0$, and $0<\alpha <r+1 - 1/\lambda_p$, we have \[ E_n(f)_{p, w_n} = O(n^{-\alpha}) \iff \omega_\varphi^{r+1}(f, n^{-1})_{p, w_n} =…
For the most general Polya urn schemes, we establish the almost sure convergence of its composition. The only requirement is that there are always enough balls of both colors, so that the extractions can be indefinitely pursued according to…
The use of numerical uncertainty representations allows better modeling of some aspects of human evidential reasoning. It also makes knowledge acquisition and system development, test, and modification more difficult. We propose that where…
When the weak value of a projector is 1, a quantum system behaves as in that eigenstate with probability 1. By definition, however, the weak value may take an anomalous value lying outside the range of probability like -1. From the…
We consider a version of the classical Ehrenfest urn model with two urns and two types of balls: regular and heavy. Each ball is selected independently according to a Poisson process having rate $1$ for regular balls and rate…
Extreme shock models have been introduced in Gut and H\"usler (1999) to study systems that at random times are subject to shock of random magnitude. These systems break down when some shock overcomes a given resistance level. In this paper…
This paper deals with strong structural controllability of linear structured systems in which the system matrices are given by zero/nonzero/arbitrary pattern matrices. Instead of assuming that the nonzero and arbitrary entries of the system…
Recommender Systems (RS), as an efficient tool to discover users' interested items from a very large corpus, has attracted more and more attention from academia and industry. As the initial stage of RS, large-scale matching is fundamental…
Weighted voting games are ubiquitous mathematical models which are used in economics, political science, neuroscience, threshold logic, reliability theory and distributed systems. They model situations where agents with variable voting…