We answer the following question: given any n ∈ N, which is the minimum number of endpoints en of a tree admitting a zero-entropy map f with a periodic orbit of period n? We prove that en = s1s2 ···sk − ∑k i=2 sisi+1 ···sk, where n = s1s2 ···sk is the decomposition of n into a product of primes such that si ≤ si+1 for 1 ≤ i < k. As a corollary, we get a criterion to decide whether a map f defin...

In this paper, we show that contraction operations preserve the homology of nD generalized maps, under some conditions. This result extends the similar one given for removal operations in [6]. Removal and contraction operations are used to propose an efficient algorithm that compute homology generators of nD generalized maps. Its principle consists in simplifying a generalized map as much as po...

We show that S. Saito’s fixed point formula serves as a powerful tool for counting the number of isolated periodic points of an area-preserving surface map admitting periodic curves. His notion of periodic curves of types I and II plays a central role in our discussion. We establish a Shub-Sullivan type result on the stability of local indices under iterations of the map, the finiteness of the ...

Our aim was to determine the roles of somatomotor activation and muscle ischemia for the tachycardia and hypertension of isometric arm contraction. Carotid-cardiac and carotid-mean arterial pressure (MAP) baroreflex response curves were determined in 10 men during rest, during isometric arm contraction at 30% of maximum, and during postcontraction ischemia. Carotid distending pressure (CDP) was...

In the present investigation of cross-striated muscle fibers of axolotl, we succeeded in observing in one field of vision of the electron microscope all the stages of myofibril contraction. This allowed us to avoid errors in establishing the sequence of individual contraction stages. Our studies reveal a new contraction stage which appears at the shortening of the sarcomere below 74 per cent of...

We show that every geodesic metric space admitting an injective continuous map into the plane as well planar graph has Nagata dimension at most two, hence asymptotic two. This relies on and answers a question in recent work by Fujiwara Papasoglu. conclude all three-dimensional Hadamard manifolds have three. As consequence, such are absolute Lipschitz retracts.

Matroids admitting an odd ear-decomposition can be viewed as natural generalizations of factor-critical graphs. We prove that a matroid representable over a field of characteristic 2 admits an odd ear-decomposition if and only if it can be represented by some space on which the induced scalar product is a non-degenerate symplectic form. We also show that, for a matroid representable over a fiel...

This paper focuses on finite-dimensional upper and lower bounds on decodable thresholds of m and binary low-density parity-check (LDPC) codes, assuming belief propagation decoding on memoryless channels. A concrete framework is presented, admitting systematic searches for new bounds. Two noise measures are considered: the Bhattacharyya noise parameter and the soft bit value for a maximum a post...