相关论文: Injectivity and the Law of Demand

Willems' fundamental lemma asserts that all trajectories of a linear time-invariant system can be obtained from a finite number of measured ones, assuming that controllability and a persistency of excitation condition hold. We show that…

It is not uncommon in analysis that existence of extremal objects is obtained via an iterative procedure: we start from a given admissible object, then modify it, then modify again etc... If being extremal means maximimizing a real valued…

A matrix is apportionable if it is similar to a matrix whose entries have equal moduli. This paper shows that all nilpotent matrices and all matrices with rank at most half their order are apportionable. General results are established and…

In a many-to-many matching model in which agents' preferences satisfy substitutability and the law of aggregate demand, we proof the General Manipulability Theorem. We result generalizes the presented in Sotomayor (1996 and 2012) for the…

Structural equation models are multivariate statistical models that are defined by specifying noisy functional relationships among random variables. We consider the classical case of linear relationships and additive Gaussian noise terms.…

In this paper we will obtain some further properties for specializations in a scheme. Using these results, we will take a picture for a scheme and a picture for a morphism of schemes. In particular, we will prove that every morphism of…

We consider the notion of herdability, a set-based reachability condition, which asks whether the state of a system can be controlled to be element-wise larger than a non-negative threshold. First a number of foundational results on…

The induction principle for natural numbers expresses that when a property holds for some natural number a and is hereditary, then it holds for all numbers greater than or equal to a. We present a similar principle for real numbers.

In this note we re-visit the fundamental question of the strong law of large numbers and central limit theorem for processes in continuous time with conditional stationary and independent increments. For convenience we refer to them as…

As mathematical induction is applied to prove statements on natural numbers, {\it continuous induction} (or, {\it real induction}) is a tool to prove some statements in real analysis.(Although, this comparison is somehow an overstatement.)…

Some classic second-order sufficient optimality conditions in the calculus of variations are shown to be equivalent, while also introducing a new equivalent second-order condition which is extremely easy to apply: simply integrate a linear…

We consider realizations of a graph in the plane such that the distances between adjacent vertices satisfy the constraints given by an edge labeling. If there are infinitely many such realizations, counted modulo rigid motions, the labeling…

We define a variant of realizability where realizers are pairs of a term and a substitution. This variant allows us to prove the normalization of a simply-typed call-by-need $$\lambda$-$calculus with control due to Ariola et al. Indeed, in…

Robotic cell injection is used for automatically delivering substances into a cell and is an integral component of drug development, genetic engineering and many other areas of cell biology. Traditionally, the correctness of functionality…

Robustness is a basic property of any control system. In the context of linear output regulation, it was proved that embedding an internal model of the exogenous signals is necessary and sufficient to achieve tracking of the desired…

Jacobian conjectures (that nonsingular implies invertible) for rational everywhere defined maps of real n-space to itself are considered, with no requirement for a constant Jacobian determinant or a rational inverse. The associated…

In the sequential decision making setting, an agent aims to achieve systematic generalization over a large, possibly infinite, set of environments. Such environments are modeled as discrete Markov decision processes with both states and…

Let F be a continuous injective map from an open subset of R^n to R^n. Assume that, for infinitely many k>1, F induces a bijection between the rational points of denominator k in the domain and those in the image (the denominator of…

We prove a conditional expectation bang-bang principle. Based on properties of the conditional expectation vector measure, we establish that the conditional expectation of a set-valued mapping coincides with the conditional expectation of…

The features of a logically sound approach to a theory of statistical reasoning are discussed. A particular approach that satisfies these criteria is reviewed. This is seen to involve selection of a model, model checking, elicitation of a…