We prove that the detection rate of n-crossing alternating links by many standard link invariants decays exponentially in n, implying that they detect alternating links with probability zero. This phenomenon applies broadly, in particular to the Jones and HOMFLYPT polynomials and integral Khovanov homology. We also use a big-data approach to analyze knots and provide evidence that, for knots as well, these invariants exhibit the same asymptotic failure of detection.

Sex comprises an intricate tangle of impulses and interactions between partners. Neuroscientists have learned a great deal about the neural mechanisms underlying sex, but questions about the processes that control the sequence of events during sex remain unanswered. While past research has identified the regions of the brain that control how mice initiate sex, other steps of copulation are still mysteries. A team of researchers in China and Japan have investigated which brain regions and neurotransmitters are responsible for different phases during sex. A paper published March 19 in the journal Neuron describes what exactly goes on in a mouse brain during sex.

We have developed a reinforcement learning agent that often finds a minimal sequence of unknotting crossing changes for a knot diagram with up to 200 crossings, hence giving an upper bound on the unknotting number. We have used this to determine the unknotting number of 57k knots. We took diagrams of connected sums of such knots with oppositely signed signatures, where the summands were overlaid. The agent has found examples where several of the crossing changes in an unknotting collection of crossings result in hyperbolic knots. Based on this, we have shown that, given knots $K$ and $K'$ that satisfy some mild assumptions, there is a diagram of their connected sum and $u(K) + u(K')$ unknotting crossings such that changing any one of them results in a prime knot. As a by-product, we have obtained a dataset of 2.6 million distinct hard unknot diagrams; most of them under 35 crossings. Assuming the additivity of the unknotting number, we have determined the unknotting number of 43 at most 12-crossing knots for which the unknotting number is unknown.

Physicists may have found a solution for the rage-inducing tangles that crop up in everything from electronics cords to necklaces: to free a single thread from a tangle of many, you must shake it not too fast and not too slow but with just the right frequency. Ishant Tiwari at the Georgia Institute of Technology in Atlanta and his colleagues created a vibrating robot to determine how to best jiggle a single thread from such a tangle. Human cells have a resonant frequency – and it's just barely audible

Tangles were originally introduced as a concept to formalize regions of high connectivity in graphs. In recent years, they have also been discovered as a link between structural graph theory and data science: when interpreting similarity in data sets as connectivity between points, finding clusters in the data essentially amounts to finding tangles in the underlying graphs. This paper further explores the potential of tangles in data sets as a means for a formal study of clusters. Real-world data often follow a normal distribution. Accounting for this, we develop a quantitative theory of tangles in data sets drawn from Gaussian mixtures. To this end, we equip the data with a graph structure that models similarity between the points and allows us to apply tangle theory to the data. We provide explicit conditions under which tangles associated with the marginal Gaussian distributions exist asymptotically almost surely. This can be considered as a sufficient formal criterion for the separabability of clusters in the data.

Medical Imaging Informatics and Artificial Intelligence at UCSF is headed by Dr. Dugyu Tosun-Torgut and brings together world-class researchers from multiple disciplines in order to find new, innovative ways to use artificial intelligence and imaging for medical diagnosis. By uniting neurologists, engineers, and data scientists Medical Imaging Informatics and Artificial Intelligence will be extremely impactful in increasing the scope of our current imaging systems when it comes to the brain. The Medical Imaging Informatics and Artificial Intelligence Lab at UCSF aims to foster a truly collaborative environment. All team members are expected to contribute and participate in meaningful ways as we seek to discover novel new ways to utilize technology to better diagnose and treat patients. We value long term partnerships and create a trusting environment for all to succeed.

With the increasing ubiquity of autonomous robotic solutions, the interest in their connectivity and in the cooperation within multi-robot systems is rising. Two aspects that are a matter of current research are robot security and secure multi-robot collaboration robust to byzantine agents. Blockchain and other distributed ledger technologies (DLTs) have been proposed to address the challenges in both domains. Nonetheless, some key challenges include scalability and deployment within real-world networks. This paper presents an approach to integrating IOTA and ROS 2 for more scalable DLT-based robotic systems while allowing for network partition tolerance after deployment. This is, to the best of our knowledge, the first implementation of IOTA smart contracts for robotic systems, and the first integrated design with ROS 2. This is in comparison to the vast majority of the literature which relies on Ethereum. We present a general IOTA+ROS 2 architecture leading to partition-tolerant decision-making processes that also inherit byzantine tolerance properties from the embedded blockchain structures. We demonstrate the effectiveness of the proposed framework for a cooperative mapping application in a system with intermittent network connectivity. We show both superior performance with respect to Ethereum in the presence of network partitions, and a low impact in terms of computational resource utilization. These results open the path for wider integration of blockchain solutions in distributed robotic systems with less stringent connectivity and computational requirements.

Anyone who has ever had to brush long hair will know that trying to get the knots out can be a nightmare. But mathematicians have now proved what many have suspected for some time – that the key to freeing the tangles is beginning at the ends and moving upwards the roots. Harvard researchers created a model that simulated two helically entwined filaments (similar to a strand of DNA) to represent a tangle of hair, and analysed different ways of'brushing' it so the hairs became free. Their results, published in the journal Soft Matter, revealed short brush strokes that start at the'free' end of the hair and move towards the'clamped' end are most effective. Experiments and simulations show the'tine' (representing a prong of the brush) moving along the double helix from the clamped end towards the free end'Using this minimal model, we study the detangling of the double helix via a single stiff tine (prong) that moves along it, leaving two untangled filaments in its wake,' said Plumb-Reyes, a graduate student at SEAS. 'We measured the forces and deformations associated with combing and then simulated it numerically.'

Any study of memory is, in the main, a study of its frailty. In "Remember," an engrossing survey of the latest research, Lisa Genova explains that a healthy brain quickly forgets most of what passes into conscious awareness. The fragments of experience that do get encoded into long-term memory are then subject to "creative editing." To remember an event is to reimagine it; in the reimagining, we inadvertently introduce new information, often colored by our current emotional state. It is sobering to realize that three out of four prisoners who are later exonerated through DNA evidence were initially convicted on the basis of eyewitness testimony.

We introduce a new approach to clustering by using tangles, a tool that originates in mathematical graph theory. Given a collection of "weak partitions" of a data set, tangles provide a framework to aggregate these weak partitions such that they "point in the direction of a cluster". As a result, a cluster is softly characterized by a set of consistent pointers. This mechanism provides a highly flexible way of solving soft clustering problems in a variety of setups, ranging from questionnaires over community detection in graphs to clustering points in metric spaces. Conceptually, tangles have many intriguing properties: (1) Similar to boosting, which combines many weak classifiers to a strong classifier, tangles provide a formal way to combine many weak partitions to obtain few strong clusters. (2) In terms of computational complexity, tangles allow us to use simple, fast algorithms to produce the weak partitions. The complexity of identifying the strong partitions is dominated by the number of weak partitions, not the number of data points, leading to an interesting trade-off between the two. (3) If the weak partitions are interpretable, so are the strong partitions induced by the tangles, resulting in one of the rare algorithms to produce interpretable clusters. (4) The output of tangles is of a hierarchical nature, inducing the notion of a soft dendrogram that can be helpful in data visualization.