Dynamics of Epidemics

This article examines how diseases on random networks spread in time. The disease is described by a probability distribution function for the number of infected and recovered individuals, and the probability distribution is described by a generating function. The time development of the disease is obtained by iterating the generating function. In cases where the disease can expand to an epidemic, the probability distribution function is the sum of two parts; one which is static at long times, and another whose mean grows exponentially. The time development of the mean number of infected individuals is obtained analytically. When epidemics occur, the probability distributions are very broad, and the uncertainty in the number of infected individuals at any given time is typically larger than the mean number of infected individuals.Comment: 4 pages and 3 figure

Temperature-Robust Neural Function from Activity-Dependent Ion Channel Regulation

Many species of cold-blooded animals experience substantial and rapid fluctuations in body temperature. Because biological processes are differentially temperature dependent, it is difficult to understand how physiological processes in such animals can be temperature robust [1–8]. Experiments have shown that core neural circuits, such as the pyloric circuit of the crab stomatogastric ganglion (STG), exhibit robust neural activity in spite of large (20$^{\circ}$C) temperature fluctuations [3, 5, 7, 8]. This robustness is surprising because (1) each neuron has many different kinds of ion channels with different temperature dependencies (Q$_{10}$s) that interact in a highly nonlinear way to produce firing patterns and (2) across animals there is substantial variability in conductance densities that nonetheless produce almost identical firing properties. The high variability in conductance densities in these neurons [9, 10] appears to contradict the possibility that robustness is achieved through precise tuning of key temperature-dependent processes. In this paper, we develop a theoretical explanation for how temperature robustness can emerge from a simple regulatory control mechanism that is compatible with highly variable conductance densities [11–13]. The resulting model suggests a general mechanism for how nervous systems and excitable tissues can exploit degenerate relationships among temperature-sensitive processes to achieve robust function.Charles A. King Trust Fellowship, National Institutes of Health (Grant IDs: NS 081013, NIH 1P01NS079419

Steady-State Cracks in Viscoelastic Lattice Models II

We present the analytic solution of the Mode III steady-state crack in a square lattice with piecewise linear springs and Kelvin viscosity. We show how the results simplify in the limit of large width. We relate our results to a model where the continuum limit is taken only along the crack direction. We present results for small velocity, and for large viscosity, and discuss the structure of the critical bifurcation for small velocity. We compute the size of the process zone wherein standard continuum elasticity theory breaks down.Comment: 17 pages, 3 figure

Disparity between General Symptom Relief and Remission Criteria in the Positive and Negative Syndrome Scale (PANSS): A Post-treatment Bifactor Item Response Theory Model.

Objective: Total scale scores derived by summing ratings from the 30-item PANSS are commonly used in clinical trial research to measure overall symptom severity, and percentage reductions in the total scores are sometimes used to document the efficacy of treatment. Acknowledging that some patients may have substantial changes in PANSS total scores but still be sufficiently symptomatic to warrant diagnosis, ratings on a subset of 8 items, referred to here as the "Remission set," are sometimes used to determine if patients' symptoms no longer satisfy diagnostic criteria. An unanswered question remains: is the goal of treatment better conceptualized as reduction in overall symptom severity, or reduction in symptoms below the threshold for diagnosis? We evaluated the psychometric properties of PANSS total scores, to assess whether having low symptom severity post-treatment is equivalent to attaining Remission. Design: We applied a bifactor item response theory (IRT) model to post-treatment PANSS ratings of 3,647 subjects diagnosed with schizophrenia assessed at the termination of 11 clinical trials. The bifactor model specified one general dimension to reflect overall symptom severity, and five domain-specific dimensions. We assessed how PANSS item discrimination and information parameters varied across the range of overall symptom severity (θ), with a special focus on low levels of symptoms (i.e., θ<-1), which we refer to as "Relief" from symptoms. A score of θ=-1 corresponds to an expected PANSS item score of 1.83, a rating between "Absent" and "Minimal" for a PANSS symptom. Results: The application of the bifactor IRT model revealed: (1) 88% of total score variation was attributable to variation in general symptom severity, and only 8% reflected secondary domain factors. This implies that a general factor may provide a good indicator of symptom severity, and that interpretation is not overly complicated by multidimensionality; (2) Post-treatment, 534 individuals (about 15% of the whole sample) scored in the "Relief" range of general symptom severity, but more than twice that number (n = 1351) satisfied Remission criteria (37%). 2 in 3 Remitted patients had scores that were not in a low symptom range (corresponding to Absent or Minimal item scores); (3) PANSS items vary greatly in their ability to measure the general symptom severity dimension; while many items are highly discriminating and relatively "pure" indicators of general symptom severity (delusions, conceptual disorganization), others are better indicators of specific dimensions (blunted affect, depression). The utility of a given PANSS item for assessing a patient depended on the illness level of the patient. Conclusion: Satisfying conventional Remission criteria was not strongly associated with low levels of symptoms. The items providing the most information for patients in the symptom Relief range were Delusions, Preoccupation, Suspiciousness Persecution, Unusual Thought Content, Conceptual Disorganization, Stereotyped Thinking, Active Social Avoidance, and Lack of Judgment and Insight. Lower scores on these items (item scores ≤2) were strongly associated with having a low latent trait θ or experiencing overall symptom relief. The inter-rater agreement between Remission and Relief subjects suggested that these criteria identified different subsets of patients. Alternative subsets of items may offer better indicators of general symptom severity and provide better discrimination (and lower standard errors) for scaling individuals and judging symptom relief, where the "best" subset of items ultimately depends on the illness range and treatment phase being evaluated

Cell types, network homeostasis, and pathological compensation from a biologically plausible ion channel expression model.

How do neurons develop, control, and maintain their electrical signaling properties in spite of ongoing protein turnover and perturbations to activity? From generic assumptions about the molecular biology underlying channel expression, we derive a simple model and show how it encodes an "activity set point" in single neurons. The model generates diverse self-regulating cell types and relates correlations in conductance expression observed in vivo to underlying channel expression rates. Synaptic as well as intrinsic conductances can be regulated to make a self-assembling central pattern generator network; thus, network-level homeostasis can emerge from cell-autonomous regulation rules. Finally, we demonstrate that the outcome of homeostatic regulation depends on the complement of ion channels expressed in cells: in some cases, loss of specific ion channels can be compensated; in others, the homeostatic mechanism itself causes pathological loss of function.Charles A. King TrustThis is the final version of the article. It first appeared from Cell Press (Elsevier) via http://dx.doi.org/10.1016/j.neuron.2014.04.002

Steady-State Cracks in Viscoelastic Lattice Models

We study the steady-state motion of mode III cracks propagating on a lattice exhibiting viscoelastic dynamics. The introduction of a Kelvin viscosity $\eta$ allows for a direct comparison between lattice results and continuum treatments. Utilizing both numerical and analytical (Wiener-Hopf) techniques, we explore this comparison as a function of the driving displacement $\Delta$ and the number of transverse sites $N$. At any $N$, the continuum theory misses the lattice-trapping phenomenon; this is well-known, but the introduction of $\eta$ introduces some new twists. More importantly, for large $N$ even at large $\Delta$, the standard two-dimensional elastodynamics approach completely misses the $\eta$-dependent velocity selection, as this selection disappears completely in the leading order naive continuum limit of the lattice problem.Comment: 27 pages, 8 figure

Electron vortex beams in a magnetic field: A new twist on Landau levels and Aharonov-Bohm states

We examine the propagation of the recently-discovered electron vortex beams in a longitudinal magnetic field. We consider both the Aharonov-Bohm configuration with a single flux line and the Landau case of a uniform magnetic field. While stationary Aharonov-Bohm modes represent Bessel beams with flux- and vortex-dependent probability distributions, stationary Landau states manifest themselves as non-diffracting Laguerre-Gaussian beams. Furthermore, the Landau-state beams possess field- and vortex-dependent phases: (i) the Zeeman phase from coupling the quantized angular momentum to the magnetic field and (ii) the Gouy phase, known from optical Laguerre-Gaussian beams. Remarkably, together these phases determine the structure of Landau energy levels. This unified Zeeman-Landau-Gouy phase manifests itself in a nontrivial evolution of images formed by various superpositions of modes. We demonstrate that, depending on the chosen superposition, the image can rotate in a magnetic field with either (i) Larmor, (ii) cyclotron (double-Larmor), or (iii) zero frequency. At the same time, its centroid always follows the classical cyclotron trajectory, in agreement with the Ehrenfest theorem. Remarkably, the non-rotating superpositions reproduce stable multi-vortex configurations that appear in rotating superfluids. Our results open up an avenue for the direct electron-microscopy observation of fundamental properties of free quantum electron states in magnetic fields.Comment: 21 pages, 10 figures, 1 table, to appear in Phys. Rev.

Product recognition in store shelves as a sub-graph isomorphism problem

The arrangement of products in store shelves is carefully planned to maximize sales and keep customers happy. However, verifying compliance of real shelves to the ideal layout is a costly task routinely performed by the store personnel. In this paper, we propose a computer vision pipeline to recognize products on shelves and verify compliance to the planned layout. We deploy local invariant features together with a novel formulation of the product recognition problem as a sub-graph isomorphism between the items appearing in the given image and the ideal layout. This allows for auto-localizing the given image within the aisle or store and improving recognition dramatically.Comment: Slightly extended version of the paper accepted at ICIAP 2017. More information @project_page --> http://vision.disi.unibo.it/index.php?option=com_content&view=article&id=111&catid=7

Correlations in ion channel expression emerge from homeostatic tuning rules.

Experimental observations reveal that the expression levels of different ion channels vary across neurons of a defined type, even when these neurons exhibit stereotyped electrical properties. However, there are robust correlations between different ion channel expression levels, although the mechanisms that determine these correlations are unknown. Using generic model neurons, we show that correlated conductance expression can emerge from simple homeostatic control mechanisms that couple expression rates of individual conductances to cellular readouts of activity. The correlations depend on the relative rates of expression of different conductances. Thus, variability is consistent with homeostatic regulation and the structure of this variability reveals quantitative relations between regulation dynamics of different conductances. Furthermore, we show that homeostatic regulation is remarkably insensitive to the details that couple the regulation of a given conductance to overall neuronal activity because of degeneracy in the function of multiple conductances and can be robust to "antihomeostatic" regulation of a subset of conductances expressed in a cell.Swartz FoundationThis is the final version of the article. It first appeared from National Academy of Sciences via http://dx.doi.org/10.1073/pnas.1309966110

A Dynamic Atomistic-Continuum Method for the Simulation of Crystalline Materials

We present a coupled atomistic-continuum method for the modeling of defects and interface dynamics of crystalline materials. The method uses atomistic models such as molecular dynamics near defects and interfaces, and continuum models away from defects and interfaces. We propose a new class of matching conditions between the atomistic and continuum regions. These conditions ensure the accurate passage of large scale information between the atomistic and continuum regions and at the same time minimize the reflection of phonons at the atomistic-continuum interface. They can be made adaptive if we choose appropriate weight functions. We present applications to dislocation dynamics, friction between two-dimensional crystal surfaces and fracture dynamics. We compare results of the coupled method and the detailed atomistic model.Comment: 48 pages, 20 figure