Analysis of a continuous-time model of structural balance

It is not uncommon for certain social networks to divide into two opposing camps in response to stress. This happens, for example, in networks of political parties during winner-takes-all elections, in networks of companies competing to establish technical standards, and in networks of nations faced with mounting threats of war. A simple model for these two-sided separations is the dynamical system dX/dt = X^2 where X is a matrix of the friendliness or unfriendliness between pairs of nodes in the network. Previous simulations suggested that only two types of behavior were possible for this system: either all relationships become friendly, or two hostile factions emerge. Here we prove that for generic initial conditions, these are indeed the only possible outcomes. Our analysis yields a closed-form expression for faction membership as a function of the initial conditions, and implies that the initial amount of friendliness in large social networks (started from random initial conditions) determines whether they will end up in intractable conflict or global harmony.Comment: 12 pages, 2 figure

The energy landscape of social balance

We model a close-knit community of friends and enemies as a fully connected network with positive and negative signs on its edges. Theories from social psychology suggest that certain sign patterns are more stable than others. This notion of social "balance" allows us to define an energy landscape for such networks. Its structure is complex: numerical experiments reveal a landscape dimpled with local minima of widely varying energy levels. We derive rigorous bounds on the energies of these local minima and prove that they have a modular structure that can be used to classify them.Comment: 4 pages, 3 figure

Invariant submanifold for series arrays of Josephson junctions

We study the nonlinear dynamics of series arrays of Josephson junctions in the large-N limit, where N is the number of junctions in the array. The junctions are assumed to be identical, overdamped, driven by a constant bias current and globally coupled through a common load. Previous simulations of such arrays revealed that their dynamics are remarkably simple, hinting at the presence of some hidden symmetry or other structure. These observations were later explained by the discovery of (N - 3) constants of motion, each choice of which confines the resulting flow in phase space to a low-dimensional invariant manifold. Here we show that the dimensionality can be reduced further by restricting attention to a special family of states recently identified by Ott and Antonsen. In geometric terms, the Ott-Antonsen ansatz corresponds to an invariant submanifold of dimension one less than that found earlier. We derive and analyze the flow on this submanifold for two special cases: an array with purely resistive loading and another with resistive-inductive-capacitive loading. Our results recover (and in some instances improve) earlier findings based on linearization arguments.Comment: 10 pages, 6 figure

Neutrophils in cancer: neutral no more

Neutrophils are indispensable antagonists of microbial infection and facilitators of wound healing. In the cancer setting, a newfound appreciation for neutrophils has come into view. The traditionally held belief that neutrophils are inert bystanders is being challenged by the recent literature. Emerging evidence indicates that tumours manipulate neutrophils, sometimes early in their differentiation process, to create diverse phenotypic and functional polarization states able to alter tumour behaviour. In this Review, we discuss the involvement of neutrophils in cancer initiation and progression, and their potential as clinical biomarkers and therapeutic targets

The importance of LDL-C lowering in atherosclerotic cardiovascular disease prevention: Lower for longer is better

Cumulative exposure to low-density lipoprotein cholesterol (LDL-C) is a key driver of atherosclerotic cardiovascular disease (ASCVD) risk. An armamentarium of therapies to achieve robust and sustained reduction in LDL-C can reduce ASCVD risk. The gold standard for LDL-C assessment is ultracentrifugation but in routine clinical practice LDL-C is usually calculated and the most accurate calculation is the Martin/Hopkins equation. For primary prevention, consideration of estimated ASCVD risk frames decision making regarding use of statins and other therapies, and tools such as risk enhancing factors and coronary artery calcium enable tailoring of risk assessment and decision making. In patients with diabetes, lipid lowering therapy is recommended in most patients to reduce ASCVD risk with an opportunity to tailor therapy based on other risk factors. Patients with primary hypercholesterolemia and familial hypercholesterolemia (FH) with baseline LDL-C greater than or equal to 190 mg/dL are at elevated risk, and LDL-C lowering with high-intensity statin therapy is often combined with non-statin therapies to prevent ASCVD. Secondary prevention of ASCVD, including in patients with prior myocardial infarction or stroke, requires intensive lipid lowering therapy and lifestyle modification approaches. There is no established LDL-C level below which benefit ceases or safety concerns arise. When further LDL-C lowering is required beyond lifestyle modifications and statin therapy, additional medications include oral ezetimibe and bempedoic acid, or injectables such as PCSK9 monoclonal antibodies or siRNA therapy. A novel agent that acts independently of hepatic LDL receptors is evinacumab, which is approved for patients with homozygous FH. Other emerging agents are targeted at Lp(a) and CETP. In light of the expanding lipid treatment landscape, this manuscript reviews the importance of early, intensive, and sustained LDL-C-lowering for primary and secondary prevention of ASCVD