If we track atom occurrences in classical propositional proofs in deep inference, we see that they can form cyclic structures between cuts and identity steps. These cycles are an obstacle to a very natural form of normalisation, that simply unfolds all the contractions in a proof. This mechanism, which we call ‘decomposition’, has many points of contact with explicit substitutions in lambda cal...

In this paper we investigate how certain results related to the HananiTutte theorem can be lifted to orientable surfaces of higher genus. We give a new simple, geometric proof that the weak Hanani-Tutte theorem is true for higher-genus surfaces. We extend the proof to prove that bipartite generalized thrackles in a surface S can be embedded in S. We also show that a result of Pach and Tóth that...

Removing Shadows from Images

Timed automata are among the most widely studied models for real-time systems. Silent transitions, i.e., "-transitions, have already been proposed in the original paper on timed automata by Alur and Dill 2]. In 7] it is shown that "-transitions can be removed, if they do not reset clocks; moreover "-transitions strictly increase the power of timed automata, if there is a self-loop containing "-...

The Prediction Error Filter (PEF) is a widely used tool in various geophysical applications such as signal-noise separation and interpolation of missing data. Over the years, SEP has developed tools to estimate non-stationary Prediction Error Filters. Non-stationary PEFs are successfully used for multiple removal, ground-roll attenuation, and in other geophysical problems. I apply a non-station...

This paper describes a method for the detection and removal of shadows in RGB images. The shadows are with hard borders. The proposed method begins with a segmentation of the color image. It is then decided if a segment is a shadow by examination of its neighboring segments. We use the method introduced in Finlayson et. al. [1] to remove the shadows by zeroing the shadow’s borders in an edge re...

In this study, a mathematical model is developed based on algebraic equations which is capable of generating artificially normal events of electrocardiogram (ECG) signals such as P-wave, QRS complex, and T-wave. This model can also be implemented for the simulation of abnormal phenomena of electrocardiographic signals such as ST-segment episodes (i.e. depression, elevation, and sloped ascending...

Monoclonal antibodies (mAbs) are increasingly being used to treat cancer. In response to mAb therapy, we have identified macrophages in the liver as major effector cells removing circulating tumor cells via antibody-dependent phagocytosis, an immune cell-mediated process that prevented liver metastasis. This discovery extends our understanding of the mechanisms of mAb therapy, and may help to o...

Starting with an algorithm to turn lists into full trees which uses non-obvious invariants and partial functions, we progressively encode the invariants in the types of the data, removing most of the burden of a correctness proof. The invariants are encoded using non-uniform inductive types which parallel numerical representations in a style advertised by Okasaki, and a small amount of dependen...