We investigate combinatorial commutation properties for reordering a sequence consisting of two kinds of steps and for separating the well-foundedness of their combination into well-foundedness of each. A weakened version of the lifting property—requiring only an eventual lifting, is used for proving wellfoundedness of such unions of relations. In particular, it is used to show the well-founded...

Cancer recurrence is associated with treatment failure and is the main cause of death, 1 and thus remains to be a major clinical challenge. elevated level of the cyclin-dependent kinase 1 (CDK1) correlates with cancer recurrence and treatment resistance in patients with breast cancer or colorectal cancer. 2,3 it is proposed that defects in CDKs may lead to the accumulated genetic defects, which...

We propose a simple model for the behaviour of longterm investors on a stock market. It consists of three particles that represent the stock’s current price and the buyers’, respectively sellers’, opinion about the right trading price. As time evolves, both groups of traders update their opinions with respect to the current price. The speed of updating is controled by a parameter γ; the price p...

Even though mastocytoma P815 often undergoes a nearly complete rejection in syngeneic mice, the tumor cells almost always escape to form progressive tumors. We found that this was not due to the establishment of an immunosuppressed state because genetically marked P815 cells, that were injected in mice where tumor escape was occurring, were readily rejected. An analysis of escaping tumor cell p...

The Trypanosomatidae family includes the genera Trypanosoma and Leishmania, protozoan parasites displaying complex digenetic life cycles requiring a vertebrate host and an insect vector. Trypanosoma brucei gambiense, Trypanosoma cruzi, and Leishmania spp. are important human pathogens causing human African trypanosomiasis (HAT or sleeping sickness), Chagas' disease, and various clinical forms o...

We investigate some useful strategies for solving a variety of hard search problems. In the process we identify weaknesses in the standard CSP formalisation of such problems. 1 Search in Artificial Intelligence A basic challenge in Artificial Intelligence is to understand how people solve problems. In 1968 Herbert Simon wrote [14]: Problem solving is often described as a search through a vast m...

The Gripon-Berrou neural network (GBNN) is a recently invented recurrent neural network embracing a LDPClike sparse encoding setup which makes it extremely resilient to noise and errors. A natural use of GBNN is as an associative memory. There are two activation rules for the neuron dynamics, namely SUM-OF-SUM and SUM-OF-MAX. The latter outperforms the former in terms of retrieval rate by a hug...

We analyze stochastic gradient descent for optimizing non-convex functions. In many cases for non-convex functions the goal is to find a reasonable local minimum, and the main concern is that gradient updates are trapped in saddle points. In this paper we identify strict saddle property for non-convex problem that allows for efficient optimization. Using this property we show that from an arbit...