Philadelphia, PA—Engineering has always taken cues from biology. Natural organisms and systems have done well at evolving to perform tasks and achieve objectives within the limits set by nature and physics.
That is one of the reasons Anette Hosoi, professor of mechanical engineering at the Massachusetts Institute of Technology, studies snails. Snails can move in any direction—horizontally, vertically, and upside down—on various surfaces, be it sand, shells, tree barks or slick walls and smooth glass. One of the reasons for this is the sticky substance on their underbellies, which acts as a powerful lubricant and reduces friction during movement. Read the rest of this entry »
Philadelphia, PA—A photo captures only as much as the camera in use will allow, and is therefore limited by the field of view of the camera’s lens. In the case of smartphones and many advanced cameras, the view from the lens is much smaller than the view from your own eyes.
Panoramic photographs were invented to capture large objects or scenes that could not otherwise fit within the constraints of a single photo. Panoramic photography is achieved through image stitching, a process that combines two or more photographs, seamlessly blending input images with overlapping regions into one picture. A paper published by Wei Wang and Michael Ng in the SIAM Journal on Imaging Sciences this summer aims to develop an algorithm for image stitching.
Will the next strike be near or far away?
Philadelphia, PA—One way to study criminal behavior and predict a criminal’s next move is by analyzing his or her movement. Several mathematical models have addressed this in detail, in particular, the UCLA “burglary hotspot” model, also the topic of a previous Nugget published by the Society for Industrial and Applied Mathematics (SIAM).
In a paper published last month in the SIAM Journal on Applied Mathematics, authors Sorathan Chaturapruek, Jonah Breslau, Daniel Yazdi, Theodore Kolokolnikov, and Scott McCalla propose a mathematical model that analyzes criminal movement in terms of a Lévy flight, a pattern in which criminals tend to move locally as well as in large leaps to other areas. This closely replicates daily human commute in big cities. Read the rest of this entry »
Using math models to make predictions
Philadelphia, PA—The greater the plant density in a given area, the greater the amount of rainwater that seeps into the ground. This is due to a higher presence of dense roots and organic matter in the soil. Since water is a limited resource in many dry ecosystems, such as semi-arid environments and semi-deserts, there is a benefit to vegetation to adapt by forming closer networks with little space between plants.
Hence, vegetation in semi-arid environments (or regions with low rainfall) self-organizes into patterns or “bands.” The pattern formation occurs where stripes of vegetation run parallel to the contours of a hill, and are interlaid with stripes of bare ground. Banded vegetation is common where there is low rainfall. In a paper published last month in the SIAM Journal on Applied Mathematics, author Jonathan A. Sherratt uses a mathematical model to determine the levels of precipitation within which such pattern formation occurs. Read the rest of this entry »
Philadelphia, PA—One of the lesser known concerns about commercial aircraft is their stability on the ground during taxiing, takeoff, and landing. During these processes, planes must maintain stability under various operating conditions. However, in some situations, the aircraft landing gear displays unwanted oscillations, which are referred to as shimmy oscillations.
In a paper published last month in the SIAM Journal on Applied Dynamical Systems, authors Chris Howcroft, Bernd Krauskopf, Mark Lowenberg, and Simon Neild study the dynamics of aircraft landing gear using nonlinear models. The dynamics of landing gear shimmy and the wheel-ground interaction are fundamentally nonlinear. Read the rest of this entry »
Philadelphia, PA—The first few hours to days following exposure to human immunodeficiency virus (HIV) can be of critical importance in determining if infection occurs in a patient. But the low numbers of viruses and infected cells at this stage makes it very difficult to study these events in humans or animal models.
Theoretical mathematical models can help analyze viral dynamics in this early phase, and hence offer insights into therapeutic and prevention strategies, as evidenced by a paper published last month in the SIAM Journal on Applied Mathematics.
In a paper titled Stochastic Analysis of Pre- and Postexposure Prophylaxis against HIV Infection, authors Jessica Conway, Bernhard Konrad, and Daniel Coombs present theoretical models of HIV dynamics immediately following exposure to the virus, thus providing a method to study infection and treatment at these early stages, as well as come up with preemptive strategies for prevention. Read the rest of this entry »
Philadelphia, PA—Recurrent infection is a common feature of persistent viral diseases. It includes episodes of high viral production interspersed by periods of relative quiescence. These quiescent or silent stages are hard to study with experimental models. Mathematical analysis can help fill in the gaps.
In a paper titled Conditions for Transient Viremia in Deterministic in-Host Models: Viral Blips Need No Exogenous Trigger, published last month in the SIAM Journal on Applied Mathematics, authors Wenjing Zhang, Lindi M. Wahl, and Pei Yu present a model to study persistent infections.
In latent infections (a type of persistent infection), no infectious cells can be observed during the silent or quiescent stages, which involve low-level viral replication. These silent periods are often interrupted by unexplained intermittent episodes of active viral production and release. “Viral blips” associated with human immunodeficiency virus (HIV) infections are a good example of such active periods. Read the rest of this entry »
In a paper published in the journal last month, authors Anthony Bonato, Dieter Mitsche, and Pawel Pralat describe a mathematical model to disrupt flow of information in a complex real-world network, such as a terrorist organization, using minimal resources.
Terror networks are comparable in their structure to hierarchical organization in companies and certain online social networks, where information flows in one direction from a source, which produces the information or data, downwards to sinks, which consume it. Such networks are called hierarchical social networks. Read the rest of this entry »
In a paper published last month in the SIAM/ASA Journal on Uncertainty Quantification, the father-son team of Jerome and Seth Stein describe a model that estimates the balance between costs and benefits of mitigation—efforts to reduce losses by taking action now to reduce consequences later— following natural disasters, as well as rebuilding defenses in their aftermath. Using the 2011 Tohoku earthquake in Japan as an example, the authors help answer questions regarding the kinds of strategies to employ against such rare events. Read the rest of this entry »