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A recently developed measure-theoretic framework solves a stochastic inverse problem (SIP) for models where uncertainties in model output data are predominantly due to aleatoric (i.e., irreducible) uncertainties in model inputs (i.e.,…
Solutions of the bivariate, linear errors-in-variables estimation problem with unspecified errors are expected to be invariant under interchange and scaling of the coordinates. The appealing model of normally distributed true values and…
A model is proposed of an infinite population of entities immigrating to a noncompact habitat, in which the newcomers are repelled by the already existing population. The evolution of such a population is described at micro- and mesoscopic…
We point out that the horizon problem encountered in standard text-books or review papers on cosmology is, in general, derived for world models based on Robertson-Walker line element where homogeneity and isotropy of the universe -- \`a la…
A novel formalism, called H-theory, is applied to the problem of statistical equilibrium of a hierarchical complex system with multiple time and length scales. In this approach, the system is formally treated as being composed of a small…
Accurate inference on population dynamics, such as migration and changes in population size, is essential for policymaking, resource allocation and demographic research. Traditional censuses are expensive, infrequent and not timely, leading…
The use of quantitative indicators of scientific productivity seems now quite widespread for assessing researchers and research institutions. There is a general perception, however, that these indicators are not necessarily representative…
Crowd counting based on density maps is generally regarded as a regression task.Deep learning is used to learn the mapping between image content and crowd density distribution. Although great success has been achieved, some pedestrians far…
Without unrealistic continuity and smoothness assumptions on a distributional density of one dimensional dataset, constructing an authentic possibly-gapped histogram becomes rather complex. The candidate ensemble is described via a…
This paper focuses on a class of linear Hawkes processes with general immigrants. These are counting processes with shot noise intensity, including self-excited and externally excited patterns. For such processes, we introduce the concept…
There are two notoriously hard problems in cluster analysis, estimating the number of clusters, and checking whether the population to be clustered is not actually homogeneous. Given a dataset, a clustering method and a cluster validation…
One of the major problems in modeling natural signals is that signals with very similar structure may locally have completely different measurements, e.g., images taken under different illumination conditions, or the speech signal captured…
The phase space of a typical Hamiltonian system contains both chaotic and regular orbits, mixed in a complex, fractal pattern. One oft-studied phenomenon is the algebraic decay of correlations and recurrence time distributions. For…
A general approach to selective inference is considered for hypothesis testing of the null hypothesis represented as an arbitrary shaped region in the parameter space of multivariate normal model. This approach is useful for hierarchical…
Air pollution is a major global environmental health threat, in particular for people who live or work near pollution sources. Areas adjacent to pollution sources often have high ambient pollution concentrations, and those areas are…
Universality in the behavior of complex systems often reveals itself in the form of scale-invariant distributions that are essentially independent of the details of the microscopic dynamics. A representative paradigm of complex behavior in…
Real-world complex systems are often better modeled as hypergraphs, where edges represent group interactions involving multiple entities. Understanding and quantifying homophily (similarity-driven association) in such networks is essential…
The law of allometric growth originated from biology has been widely used in urban research for a long time. Some conditional research conclusions based on biological phenomena have been erroneously transmitted in the field of urban…
One of main sources of uncertainty in modern cosmology is the present rate of the universe's expansion, H0, called the Hubble constant. Once again, different observational techniques bring about different results, causing new 'Hubble…
We propose a novel approach for density estimation called histogram trend filtering. Our estimator arises from looking at surrogate Poisson model for counts of observations in a partition of the support of the data. We begin by showing…