This is an expository paper based on Border [1]. Starting from basic convexity results, I present a proof of the so-called Equilibrium Theorem, which states the existence of a free disposal equilibrium price vector in an Arrow-Debreu economy with a continuous excess demand function.

In the mid sixties, Feldman (1966) reported on experiments on feedback control processes that stabilize the human arm. In a typical test, the elbow flexors (or extensors) would be loaded and the subject was asked to maintain a predetermined elbow angle. After a sudden decrease of the load, the forearm would settle at a new position. The experiments were repeated for the same initial elbow posit...

MODELING OF EQUILIBRIUM POINT TRAJECTORY CONTROL IN HUMAN ARM MOVEMENTS by Kai Chen The underlying concept of the Equilibrium Point Hypothesis (EPH) is that the CNS provides a virtual trajectory of joint motion, representing spacing and timing, with actual movement dynamics being produced by interactions of limb inertia, muscle viscosity and speed/position feedback from muscle spindles. To coun...

The notion of studying internal control variables instead of externally observable parameters is certainly attractive. It is what motivates neurophysiologists to stick their electrodes into various parts of the nervous system. The problem is knowing a control variable when you see one. Recorded neural activity reflects a mixture of outputs representing some kind of control to various lower cent...

Immune checkpoint inhibitors (ICIs) are a novel cancer therapy that may induce tumor regression across multiple types of cancer. There has recently been interest in combining the ICIs with other forms treatments, as not all patients benefit from monotherapy. We propose mathematical model consisting ordinary differential equations to investigate combination treatments ICI avelumab and immunostim...

0 Introduction In modern treatments of predicate calculus [2], no mention is made of states or variables up until the point where substitution is introduced. There, suddenly, the abstraction that reigned before is cast to the winds, and a substitution is defined as the result of a textual replacement of variable names by expressions. It is the purpose of this note to remedy this breach of style...

Functional programs are particularly well suited to formal manipulation by equational reasoning. In particular, it is straightforward to use calculational methods for program transformation. Well-known transformation techniques, like tupling or the introduction of accumulating parameters, can be implemented using calculation through the use of the fusion (or promotion) strategy. In this paper w...

Lenses are one the most popular approaches to define bidirectional transformations between data models. A bidirectional transformation with view-update, denoted a lens, encompasses the definition of a forward transformation projecting concrete models into abstract views, together with a backward transformation instructing how to translate an abstract view to an update over concrete models. In t...