When a random spatial noise pattern is displaced for a short distance it seems to move coherently, but when the displacement exceeds a certain value, the direction of motion cannot be clearly perceived. We measured the displacement limit (Dmax) for a two-frame sequence and found that it depended on the size of the elements comprising the random pattern, even when low spatial frequencies were re...

The problem of efficiently sampling from a set of (undirected) graphs with a given degree sequence has many applications. One approach to this problem uses a simple Markov chain, which we call the switch chain, to perform the sampling. The switch chain is known to be rapidly mixing for regular degree sequences. We prove that the switch chain is rapidly mixing for any degree sequence with minimu...

A graph G = (V,E) with a vertex set V and an edge set E is called a pairwise compatibility graph (PCG, for short) if there are a tree T whose leaf set is V , a non-negative edge weight w in T , and two non-negative reals dmin ≤ dmax such that G has an edge uv ∈ E if and only if the distance between u and v in the weighted tree (T,w) is in the interval [dmin, dmax]. PCG is a new graph class moti...

Abstract Background first case of a rare Garcin syndrome resolution in young metastatic breast cancer(BC) patient treated with hippocampal-sparing approach. Material and Methods we report 49-year-old caucasian female. The medical record review was relevant for BC diagnoses 1997, when she 26yo; complicated by bone liver metastasis appeared 2008. In March 2020, referred to our department complain...

BACKGROUND The purpose of this study was to assess predictors of mucositis in oropharyngeal and oral cavity cancer after definitive or adjuvant volumetric modulated arc radiotherapy (VMAT) +/- chemotherapy. METHODS Fifty patients were evaluated. Statistical analysis was performed for the following parameters as potential predictors of mucositis ≥ G2: total oral mucosa and oral mucosa minus ta...

A graph G is called a pairwise compatibility graph (PCG) if there exists an edge-weighted tree T and two non-negative real numbers dmin and dmax such that each leaf lu of T corresponds to a vertex u ∈ V and there is an edge (u, v) ∈ E if and only if dmin ≤ dT,w(lu, lv) ≤ dmax where dT,w(lu, lv) is the sum of the weights of the edges on the unique path from lu to lv in T . In this note, we show ...

A graph G = (V, E) is a pairwise compatibility graph (PCG) if there exists an edgeweighted tree T and two non-negative real numbers dmin and dmax such that each leaf u of T is a node of V and there is an edge (u, v) ∈ E if and only if dmin ≤ dT (u, v) ≤ dmax where dT (u, v) is the sum of weights of the edges on the unique path from u to v in T . The main issue on these graphs consists in charac...

Abstract Supercooled large drop (SLD) icing poses a unique hazard for aircraft and has resulted in new regulations regarding certification to fly regions of known or forecast SLD conditions. The define two categories based upon the maximum supercooled liquid water diameter (Dmax): freezing drizzle (100–500 μm) rain (> 500 μm). Recent upgrades U.S. operational numerical weather prediction mod...

We present an efficient method for collision detection in the black-box KDS model for a set S of n objects in the plane. In this model we receive the object locations at regular time steps and we know a bound dmax on the maximum displacement of any object within one time step. Our method maintains, in O((λ+k)n) time per time step, a compressed quadtree on the bounding-box vertices of the object...