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What is the effect of punching holes at random in an infinite tensed membrane? When will the membrane still support tension? This problem was introduced by Connelly in connection with applications of rigidity theory to natural sciences. The answer clearly depends on the shapes and the distribution of the holes. We briefly outline a mathematical theory of tension based on graph rigidity theory and
Det vaga begreppet barnets bästa är beroende av samhällets utveckling och hur vi ser på barn – ibland fortfarande som ägodelar. Detta är fortfarande särskilt framträdande i den sociala barnlagstiftningen.The nebolous concept of the best interests of the child is dependent of the development of society and how we view children - sometimes still as possessions. This is still particularly prominent in social children's welfare legislation.
We study the continuous time integer valued process Xt, t ≥ 0, which jumps to each of its two nearest neighbors at the rate of one plus the total time the process has previously spent at that neighbor. We show that the proportion of the time before t which this process spends at integers j converges to positive random variables Vj, which sum to one, and whose joint distribution is explicitly descr
We introduce a new class of bootstrap percolation models where the local rules are of a geometric nature as opposed to simple counts of standard bootstrap percolation. Our geometric bootstrap percolation comes from rigidity theory and convex geometry. We outline two percolation models: a Poisson model and a lattice model. Our Poisson model describes how defects - holes is one of the possible inter
We investigate individual packet delay in a model of data networks with table-free, partial table and full table routing. We present analytical estimation for the average packet delay in a network with small partial routing table. Dependence of the delay on the size of the network and on the size of the partial routing table is examined numerically. Consequences for network scalability are discuss
Vertex-reinforced random walk (VRRW), defined by Pemantle, is a random process in a continuously changing environment which is more likely to visit states it has visited before. We consider VRRW on arbitrary graphs and show that on almost all of them, VRRW visits only finitely many vertices with a positive probability. We conjecture that on all graphs of bounded degree, this happens with probabili
A stochastic process called vertex-reinforced random walk (VRRW) is defined in Pemantle [Ann. Probab. 16 1229-1241]. We consider this process in the case where the underlying graph is an infinite chain (i.e., the one-dimensional integer lattice). We show that the range is almost surely finite, that at least five points are visited infinitely often almost surely and that with positive probability t
We consider a Markov chain on a countable state space, on which is placed a random field of traps, and ask whether the chain gets trapped almost surely. We show that the quenched problem (when the traps are fixed) is equivalent to the annealed problem (when the traps are updated each unit of time) and give a criterion for almost sure trapping versus positive probability of nontrapping. The hypothe
Thin-film thermocouples (TFTCs) are critical for real-time temperature monitoring in advanced manufacturing processes where conventional sensors fail due to spatial constraints or complex geometries. This study develops K-type TFTCs on stainless steel 316 L substrates with optimized SiO₂/SiO insulation layers for industrial deployment. In particular, two types of stainless steel substrates were in
We consider a nearest-neighbor stochastic process on a rooted tree G which goes toward the root with probability 1 − ε when it visits a vertex for the first time. At all other times it behaves like a simple random walk on G. We show that for all ε ≥ 0 this process is transient. Also we consider a generalization of this process and establish its transience in some cases.
The purpose of this short report is to introduce a branching random walk in random environment on $Z^d$ where particles perform independent simple random walks and branch according to a law that is obtained by fixing branching numbers at each point of $Z^d$. These numbers represent a realization of an integer-valued random field on $Z^d$ with the value at each point being independent of those at o
In this paper we study random walks with branching. We introduce the notion of recurrence and transience for these processes and provide criteria for them. For Lamperti problem and many-dimensional random walk with branching we nd the critical (for transience vs. recurrence) speed of decaying of the average number of o -springs at a point with respect to the distance from it to the origin.
Predicting live birth after the first IVF/ICSI treatment is challenging, as many factors may interactto affect IVF/ICSI outcomes. Adenomyosis is one factor that impacts live birth rates. Machinelearning algorithms have been shown valuable for detecting complex dependencies and predictingoutcomes in different clinical settings. We aimed to develop a prediction model for live birth afterIVF/ICSI trePredicting live birth after the first IVF/ICSI treatment is challenging, as many factors may interact to affect IVF/ICSI outcomes. Adenomyosis is one factor that impacts live birth rates. Machine learning algorithms have been shown valuable for detecting complex dependencies and predicting outcomes in different clinical settings. We aimed to develop a prediction model for live birth after IVF/ICSI
Volatile organic compounds (VOCs) include many types of organic compounds, such as alkanes, olefins, aldehydes, etc. They have attracted widespread attention in various fields such as food and flavor analysis, environmental and atmospheric research, safety, or healthcare. Developing efficient, practical, and high-value industrial VOC utilization technologies is crucial for sustainable social and h
The selective oxidation of alcohols to corresponding carbonyl compounds is essential in academia and industry. Benzil and BHMF have emerged as important classes of carbonyl compounds that have shown promising applications in materials and drug intermediates, especially in sustainable bio-based plastics. The traditional selective oxidation process generally uses equivalent amounts of oxidants or to
The introduction discusses the concepts of dynasty and state formation and their interrelated nature. It stresses the need to define the concept of dynasty as a kinship group with an acute sense of historical continuity, claiming the right to rule a certain territory and manifesting this claim in political, social and cultural ways; and the related concept of dynasty formation as the acts, conscio
TiSe2 has long been considered one of the best candidate materials to host the elusive excitonic insulator (EI) phase. However, a finite coupling to the lattice can generically be expected, while a lack of "smoking-gun"signatures for the importance of the electron-hole interaction in driving the phase transition has rendered it challenging to distinguish the EI from the conventional charge-density
