The shortest path problem is formulated as an l1-regularized regression problem, known as lasso. Based on this formulation, a connection is established between Dijkstra's shortest path algorithm and the least angle regression (LARS) for the lasso problem. Specifically, the solution path of the lasso problem, obtained by varying the regularization parameter from infinity to zero (the regularization path), corresponds to shortest path trees that appear in the bi-directional Dijkstra algorithm.

The purpose of this work is to make a case for epidemiological models with fractional exponent in the contribution of sub-populations to the incidence rate. More specifically, we question the standard assumption in the literature on epidemiological models, where the incidence rate dictating propagation of infections is taken to be proportional to the product between the infected and susceptible sub-populations; a model that relies on strong mixing between the two groups and widespread contact between members of the groups. We contend, that contact between infected and susceptible individuals, especially during the early phases of an epidemic, takes place over a (possibly diffused) boundary between the respective sub-populations. As a result, the rate of transmission depends on the product of fractional powers instead. The intuition relies on the fact that infection grows in geographically concentrated cells, in contrast to the standard product model that relies on complete mixing of the susceptible to infected sub-populations. We validate the hypothesis of fractional exponents (1) by numerical simulation for disease propagation in graphs imposing a local structure to allowed disease transmissions and (2) by fitting the model to the JHU CSSE COVID-19 Data for the period Jan-22-20 to April-30-20, for the countries of Italy, Germany, France, and Spain.

Classical thermodynamics aimed to quantify the efficiency of thermodynamic engines, by bounding the maximal amount of mechanical energy produced, compared to the amount of heat required. While this was accomplished early on, by Carnot and Clausius, the more practical problem to quantify limits of power that can be delivered, remained elusive due to the fact that quasistatic processes require infinitely slow cycling, resulting in a vanishing power output. Recent insights, drawn from stochastic models, appear to bridge the gap between theory and practice in that they lead to physically meaningful expressions for the dissipation cost in operating a thermodynamic engine over a finite time window. Indeed, the problem to optimize power can be expressed as a stochastic control problem. Building on this framework of stochastic thermodynamics we derive bounds on the maximal power that can be drawn by cycling an overdamped ensemble of particles via a time-varying potential while alternating contact with heat baths of different temperature (Tc cold, and Th hot). Specifically, assuming a suitable bound M on the spatial gradient of the controlling potential, we show that the maximal achievable power is bounded by [Formula presented]. Moreover, we show that this bound can be reached to within a factor of [Formula presented] by operating the cyclic thermodynamic process with a quadratic potential.

The purpose of this work is to make a case for epidemiological models with fractional exponent in the contribution of sub-populations to the transmission rate. More specifically, we question the standard assumption in the literature on epidemiological models, where the transmission rate dictating propagation of infections is taken to be proportional to the product between the infected and susceptible sub-populations; a model that relies on strong mixing between the two groups and widespread contact between members of the groups. We content, that contact between infected and susceptible individuals, especially during the early phases of an epidemic, takes place over a (possibly diffused) boundary between the respective sub-populations. As a result, the rate of transmission depends on the product of fractional powers instead. The intuition relies on the fact that infection grows in geographically concentrated cells, in contrast to the standard product model that relies on complete mixing of the susceptible to infected sub-populations. We validate the hypothesis of fractional exponents i) by numerical simulation for disease propagation in graphs imposing a local structure to allowed disease transmissions and ii) by fitting the model to a COVID-19 data set provided by John Hopkins University (JHUCSSE) for the period Jan-31-20 to Mar-24-20, for the countries of Italy, Germany, Iran, and France.

The common saying, that information is power, takes a rigorous form in stochastic thermodynamics, where a quantitative equivalence between the two helps explain the paradox of Maxwell's demon in its ability to reduce entropy. In this letter, we build on earlier work on the interplay between the relative cost and benefits of information in producing work in cyclic operation of thermodynamic engines (by Sandberg et al. 2014). Specifically, we study the general case of overdamped particles in a time-varying potential (control action) in feedback that utilizes continuous measurements (nonlinear filtering) of a thermodynamic ensemble, to produce suitable adaptations of the second law of thermodynamics that involve information.

We study thermodynamic processes in contact with a heat bath that may have an arbitrary time-varying periodic temperature profile. Within the framework of stochastic thermodynamics, and for models of thermodynamic engines in the idealized case of underdamped particles in the low-friction regime subject to a harmonic potential, we derive explicit bounds as well as optimal control protocols that draw maximum power and achieve maximum efficiency at any specified level of power.

The context of the present paper is stochastic thermodynamics-an approach to nonequilibrium thermodynamics rooted within the broader framework of stochastic control. In contrast to the classical paradigm of Carnot engines, we herein propose to consider thermodynamic processes with periodic continuously varying temperature of a heat bath and study questions of maximal power and efficiency for two idealized cases, overdamped (first-order) and underdamped (second-order) stochastic models. We highlight properties of optimal periodic control, derive and numerically validate approximate formulae for the optimal performance (power and efficiency).

A typical model for a gyrating engine consists of an inertial wheel powered by an energy source that generates an angle-dependent torque. Examples of such engines include a pendulum with an externally applied torque, Stirling engines, and the Brownian gyrating engine. Variations in the torque are averaged out by the inertia of the system to produce limit cycle oscillations. While torque generating mechanisms are also ubiquitous in the biological world, where they typically feed on chemical gradients, inertia is not a property that one naturally associates with such processes. In the present work, seeking ways to dispense of the need for inertial effects, we study an inertia-less concept where the combined effect of coupled torque-producing components averages out variations in the ambient potential and helps overcome dissipative forces to allow sustained operation for vanishingly small inertia. We exemplify this inertia-less concept through analysis of two of the aforementioned engines, the Stirling engine, and the Brownian gyrating engine. An analogous principle may be sought in biomolecular processes as well as in modern-day technological engines, where for the latter, the coupled torque-producing components reduce vibrations that stem from the variability of the generated torque.