Related papers: Dimer lambda_3 = .453 +/- .001 and Some Other Very…
In a previous paper an asymptotic expansion for lambda_d in powers of 1/d was developed. The results of computer computations for some terms in the expansion, as well as various quantities associated to the expansion, are herein presented.…
In the past few years we have derived asymptotic expansions for lambda_d of the dimer problem and lambda_d(p) of the monomer-dimer problem. The many expansions so far computed are collected herein. We shine a light on results in two…
We offer a conjecture on sharp estimation of a definite improper integral depend on a parameter $\lambda \in (0,+\infty)$ by means of given estimate of other definite integral depend on parameters $t\in [0,+\infty)$ and $\lambda$. Such…
Coherent lower previsions are general probabilistic models allowing incompletely specified probability distributions. However, for complete description of a coherent lower prevision -- even on finite underlying sample spaces -- an infinite…
The dimer problem arose in a thermodynamic study of diatomic molecules, and was abstracted into one of the most basic and natural problems in both statistical mechanics and combinatoric mathematics. Given a rectangular lattice of volume V…
We continue our study on the logarithmic balanced model metric initiated in our previous work. By a non-trivial refinement of the set of tools developed in our previous work, we are able to confirm partially a conjecture we made in our…
We derive an (almost) guaranteed upper bound on the error of deep neural networks under distribution shift using unlabeled test data. Prior methods either give bounds that are vacuous in practice or give estimates that are accurate on…
The use of realistic input models has gained popularity in the theory community. Assuming a realistic input model often precludes complicated hypothetical inputs, and the analysis yields bounds that better reflect the behaviour of…
Let (lambda_d)(p) be the p monomer-dimer entropy on the d-dimensional integer lattice Z^d, where p in [0,1] is the dimer density. We give upper and lower bounds for (lambda_d)(p) in terms of expressions involving (lambda_(d-1))(q). The…
We investigate the probability that a random odd composite number passes a random Fermat primality test, improving on earlier estimates in moderate ranges. For example, with random numbers to $2^{200}$, our results improve on prior…
The dimer problem arose in a thermodynamic study of diatomic molecules, and was abstracted into one of the most basic and natural problems in both statistical mechanics and combinatoric mathematics. Given a rectangular lattice of volume V…
Given an IID sample from a positive distribution, we provide a method for constructing rigorous finite sample lower confidence bounds for the expectation of the distribution. The method is based on constructing rigorous confidence regions…
Robust inference based on the minimization of statistical divergences has proved to be a useful alternative to the classical techniques based on maximum likelihood and related methods. Recently Ghosh et al. (2013) proposed a general class…
We show that the expected asymptotic for the sums $\sum_{X < n \leq 2X} \Lambda(n) \Lambda(n+h)$, $\sum_{X < n \leq 2X} d_k(n) d_l(n+h)$, and $\sum_{X < n \leq 2X} \Lambda(n) d_k(n+h)$ hold for almost all $h \in [-H,H]$, provided that…
The Latent Block Model (LBM) is a model-based method to cluster simultaneously the $d$ columns and $n$ rows of a data matrix. Parameter estimation in LBM is a difficult and multifaceted problem. Although various estimation strategies have…
This paper deals with the problem of soft guessing under log-loss distortion (logarithmic loss) that was recently investigated by [Wu and Joudeh, IEEE ISIT, pp. 466--471, 2023]. We extend this problem to soft guessing allowing errors, i.e.,…
When data contains measurement errors, it is necessary to make assumptions relating the observed, erroneous data to the unobserved true phenomena of interest. These assumptions should be justifiable on substantive grounds, but are often…
We estimate the number of integer solutions to decomposable form inequalities (both asymptotic estimates and upper bounds are provided) when the degree of the form and the number of variables are relatively prime. These estimates display…
The inflated beta regression model is widely used for modeling continuous proportions with values at the boundaries. Maximum likelihood estimation for these models is well-known for its sensitivity to outliers, which can severely distort…
Reliable uncertainty estimation is crucial for perception systems in safe autonomous driving. Recently, many methods have been proposed to model uncertainties in deep learning based object detectors. However, the estimated probabilities are…