Intermediate-Level Crossings of a First-Passage Path

We investigate some simple and surprising properties of a one-dimensional Brownian trajectory with diffusion coefficient $D$ that starts at the origin and reaches $X$ either: (i) at time $T$ or (ii) for the first time at time $T$. We determine the most likely location of the first-passage trajectory from $(0,0)$ to $(X,T)$ and its distribution at any intermediate time $t<T$. A first-passage path typically starts out by being repelled from its final location when $X^2/DT\ll 1$. We also determine the distribution of times when the trajectory first crosses and last crosses an arbitrary intermediate position $x<X$. The distribution of first-crossing times may be unimodal or bimodal, depending on whether $X^2/DT\ll 1$ or $X^2/DT\gg 1$. The form of the first-crossing probability in the bimodal regime is qualitatively similar to, but more singular than, the well-known arcsine law.Comment: 18 pages, 12 figures, IOP format; V2: various minor changes in response to referee comments. For publication in JSTA

Correlated bosons in a one-dimensional optical lattice: Effects of the trapping potential and of quasiperiodic disorder

We investigate the effect of the trapping potential on the quantum phases of strongly correlated ultracold bosons in one-dimensional periodic and quasiperiodic optical lattices. By means of a decoupling meanfield approach, we characterize the ground state of the system and its behavior under variation of the harmonic trapping, as a function of the total number of atoms. For a small atom number the system shows an incompressible Mott-insulating phase, as the size of the cloud remains unaffected when the trapping potential is varied. When the quasiperiodic potential is added the system develops a metastable-disordered phase which is neither compressible nor Mott insulating. This state is characteristic of quasidisorder in the presence of a strong trapping potential.Comment: Accepted for publication in PR

Stochastic Search with Poisson and Deterministic Resetting

We investigate a stochastic search process in one, two, and three dimensions in which $N$ diffusing searchers that all start at $x_0$ seek a target at the origin. Each of the searchers is also reset to its starting point, either with rate $r$, or deterministically, with a reset time $T$. In one dimension and for a small number of searchers, the search time and the search cost are minimized at a non-zero optimal reset rate (or time), while for sufficiently large $N$, resetting always hinders the search. In general, a single searcher leads to the minimum search cost in one, two, and three dimensions. When the resetting is deterministic, several unexpected feature arise for $N$ searchers, including the search time being independent of $T$ for $1/T\to 0$ and the search cost being independent of $N$ over a suitable range of $N$. Moreover, deterministic resetting typically leads to a lower search cost than in stochastic resetting.Comment: 23 pages, 9 figures, IOP format. Revised version: figure added, introductory text added, references added, and various minor changes incorporated. V3: Final version to appear in JSTAT. A few more references adde

Emergence of Clustering in an Acquaintance Model without Homophily

We introduce an agent-based acquaintance model in which social links are created by processes in which there is no explicit homophily. In spite of the homogeneous nature of the social interactions, highly-clustered social networks can arise. The crucial feature of our model is that of variable transitive interactions. Namely, when an agent introduces two unconnected friends, the rate at which a connection actually occurs between them depends on the number of their mutual acquaintances. As this transitive interaction rate is varied, the social network undergoes a dramatic clustering transition. Close to the transition, the network consists of a collection of well-defined communities. As a function of time, the network can also undergo an \emph{incomplete} gelation transition, in which the gel, or giant cluster, does not constitute the entire network, even at infinite time. Some of the clustering properties of our model also arise, but in a more gradual manner, in Facebook networks. Finally, we discuss a more realistic variant of our original model in which there is a soft cutoff in the rate of transitive interactions. With this variant, one can construct network realizations that quantitatively match Facebook networks.Comment: 16 pages, 14 figures, IOP format. Version 2: final form for publication in JSTA

Generation of frequency sidebands on single photons with indistinguishability from quantum dots

Generation and manipulation of the quantum state of a single photon is at the heart of many quantum information protocols. There has been growing interest in using phase modulators as quantum optics devices that preserve coherence. In this Letter, we have used an electro-optic phase modulator to shape the state vector of single photons emitted by a quantum dot to generate new frequency components (modes) and explicitly demonstrate that the phase modulation process agrees with the theoretical prediction at a single photon level. Through two-photon interference measurements we show that for an output consisting of three modes (the original mode and two sidebands), the indistinguishability of the mode engineered photon, measured through the secondorder intensity correlation (g2(0)) is preserved. This work demonstrates a robust means to generate a photonic qubit or more complex state (e.g., a qutrit) for quantum communication applications by encoding information in the sidebands without the loss of coherence

A Case of Novel Coronavirus Disease 19 in a Chronic Hemodialysis Patient Presenting with Gastroenteritis and Developing Severe Pulmonary Disease.

Novel coronavirus disease 2019 (COVID-19) is a highly infectious, rapidly spreading viral disease with an alarming case fatality rate up to 5%. The risk factors for severe presentations are concentrated in patients with chronic kidney disease, particularly patients with end-stage renal disease (ESRD) who are dialysis dependent. We report the first US case of a 56-year-old nondiabetic male with ESRD secondary to IgA nephropathy undergoing thrice-weekly maintenance hemodialysis for 3 years, who developed COVID-19 infection. He has hypertension controlled with angiotensin receptor blocker losartan 100 mg/day and coronary artery disease status-post stent placement. During the first 5 days of his febrile disease, he presented to an urgent care, 3 emergency rooms, 1 cardiology clinic, and 2 dialysis centers in California and Utah. During this interval, he reported nausea, vomiting, diarrhea, and low-grade fevers but was not suspected of COVID-19 infection until he developed respiratory symptoms and was admitted to the hospital. Imaging studies upon admission were consistent with bilateral interstitial pneumonia. He was placed in droplet-eye precautions while awaiting COVID-19 test results. Within the first 24 h, he deteriorated quickly and developed acute respiratory distress syndrome (ARDS), requiring intubation and increasing respiratory support. Losartan was withheld due to hypotension and septic shock. COVID-19 was reported positive on hospital day 3. He remained in critical condition being treated with hydroxychloroquine and tocilizumab in addition to the standard medical management for septic shock and ARDS. Our case is unique in its atypical initial presentation and highlights the importance of early testing

Performance assessment of heterogeneous irrigation schemes in India

Most irrigation schemes in India are performing poorly as seen from the average irrigation efficiency in the range of 30-40% for these projects. Hence it is necessary to study the performance assessment of these schemes to investigate the reasons and improve the performance subsequently. There are different kinds of performance measures that may vary spatially over the irrigation scheme. Hence it is necessary to use a framework for finding out the final performance index (FPI) that combines important performance measures. Hence this study was undertaken. Mula Irrigation Scheme in Ahmednagar District of Maharashtra State, India was identified after verifying that most of the needed data was available. The six performance indicators viz. Productivity, Equity, Adequacy Reliability, Flexibility and Sustainability were identified as the important one for obtaining the information on the relative preference from the farmers and first three were considered for obtaining the allocation plans. The performance of different irrigation schemes is assessed with the help of Area and Water Allocation Model (AWAM). The performance measures viz. productivity, equity, adequacy and excess were obtained by formulating the irrigation strategies based on 1. Irrigation amount: Full depth irrigation (FDI), Fixed depth irrigation (FxDI) and Variable depth irrigation (VDI), 2. Irrigation frequency (14 days, 21 days, 28 days and 35 days), 3. Water distribution: Free water distribution (FWD), Equitable distribution of seasonal water (EDSW) and Equitable distribution of intra-seasonal water (EDIW) and 4. Cropping distribution (Free cropping distribution and Fixed cropping distribution). The yield response of crops to different criteria such as soil, irrigation interval, irrigation strategy and irrigation depth, were analysed. It is found for wheat grown on all considered soils, the variable irrigation depth strategy provided better performance of irrigation scheme in terms of productivity and results in higher irrigation water use efficiency. It is concluded though that the application of water according to the variable irrigation depth strategy is operationally and from a management point of view not convenient and in current situation may not be adoptable. Though the fixed depth irrigation strategy is found to be less productive based on this research for Mula irrigation scheme, it is more convenient for operation compared to other strategies as it does not involve adoption of separate schedules for different crops. In general the area and net benefit productivity values are higher in fixed depth irrigation followed by variable depth and then full depth. The productivity values are higher in case of free cropping distribution compared to fixed cropping distribution. The equitable water distribution resulted in lower productivity compared to free water distribution. No specific trend of equity with the irrigation interval was found. Equity values are higher in case of fixed depth of irrigation compared to full depth. The equity values are higher in case of fixed cropping distribution compared to free cropping. The equity values are as expected higher or unity for equitable water distribution compared to free water distribution. The adequacy values are higher in full depth of irrigation followed by variable depth irrigation and fixed depth irrigation. It is observed that the productivity and equity are almost inversely proportional to each other. Hence the hypothesis that productivity and equity conflicts with each other holds true. Further, Analytic Hierarchy Process (AHP) was used to assign weights of different performance measures by determining the farmers relative preference of different performance measures. The average weights of different performance measures (monetary productivity, equity in water distribution and adequacy) were obtained for farmers from different reaches from the weights obtained from AHP analysis, and considerable differences were found between the weights for the head, middle and tail reaches. The values of the performance indicators were obtained from the simulation-optimization modeling (AWAM model). The different indicators were combined into a final overall performance indicator (FPI) of irrigation management in an irrigation scheme from the farmers perspective. The FPI was computed for head, middle and tail reach farmers using the weights obtained from AHP by compromise programming. It is interesting to note that the strategies that best met the farmers preferences (highest FPI), were same for middle reach and tail reach farmers however it is different for head reach. It is also interesting to note that the preferences of the head, middle and tail reach farmers, irrespective of their relative location in irrigation scheme, were best met by strategies which include the equitable distribution of water. For middle and tail reach farmers, full depth irrigation would give the highest FPI, while for head reach farmers optimised fixed depth would be best. It is also seen that for head and middle reach farmers a strategy with fixed cropping distribution and free water distribution would be worst for meeting the preferences of head and middle reach farmers while for tail reach farmers a strategy with free water and free cropping distribution would be worst. The mean values of the weights for head, middle and tail reach farmers were Productivity = 0.33, Equity = 0.31 and Adequacy = 0.36. With these weights, the highest FPI (0.85) was obtained with an irrigation strategy of Full depth irrigation with free cropping and annual equity at irrigation interval of 35 days in winter and 28 days in summer . Considering the different depth of irrigations (FxDI, VDI and FDI) the VDI and FDI are practically difficult to execute due to the data required for calculations and operational requirements of the irrigation canals. Using FxDI, a strategy with high FPI (0.83) was identified as the best feasible irrigation strategy to implement for the entire irrigation scheme: Fixed depth irrigation with free cropping and annual equity at irrigation interval of 35 days in winter and 28 days in summer . It was found that this best feasible irrigation strategy for the entire scheme was not sensitive to the weights assigned to the performance measures