Fourier analysis of weekly soil moisture at Pune

The wee!..l) soil moistu re data collected at Centra l Agromcl Observat ory ICA ~ M O J . PuucJuril1~ 19 5 K·P~ S9 have been subjccctcd to Fo urie r analysis. With norm al dat a the amplit udc~ For Varillll'i dc pl h ~'"U)' between 0 .76 In I . 1.2 em of wate r Iu r first harmonic and decrease sha rply \\ ith h igher order harmonic...l he •...rlucs for fourth harm onic range from 0 .0 3 to 0 ,07 em of water o nly. UUY, C\W, the highest amplit ude forthe calendar vcars 19t'4. 19S5. IIJH7 and 19S9 i'i fou nd 10 va ry between 0 . 45 10 1. .15 ern of wat er irrespective Ill'-oi l dep ths. Under normal co ndit io n.. the ma ximu m so il moistu re nca r the soi l surface 0 .5 em dep th ! occurson 15 September while at 30 em depth. the soil moi st ure ma vim um occurs on 2-4 September. a dcluy of 9 da) s.1:, lf th e four soil dep ths co nsidered in thi s study. the first . second and third har mo nics rc pr c-sent rc..pc...Iivc 1,\~.46. 2-32 .\ 4-26 & 67-S6. 6-t 4 a r-d 1 · 6 ~,~ of total var iance res pecti ve ly for eac h of th e years 19S-4. 19S5.IIJg7 a nd t9~9 and normal dura. The cha nge in 'oil mUI..ture pattern after J une and October due In occ urrence(If southwe...t and northeast monsoon i~ wctl ref lected .

Fourier analysis of corneal Scheimpflug imaging: clinical use in keratoconus

AIM: To evaluate the clinical use of Fourier analysis of videokeratography data in the diagnosis and follow-up of keratoconus (KC). METHODS: We conducted a chart review of consecutive patients presented to our cornea clinic. A team of two experienced cornea specialists divided the patients into three groups: normal cornea, forme fruste KC (FFKC), and clinical KC. The exclusion criteria were a history of previous ocular surgery, any accompanying corneal pathology other than KC, high myopia (>6.00 diopters), amblyopia, pregnancy, breastfeeding, or any current autoimmune disease. The data of Fourier series harmonic analysis were evaluated for their diagnostic capacity using the receiver operating characteristic (ROC) curve. A binary logistic regression analysis was also conducted to construct a diagnostic model. A total of 259 eyes showed progression in the clinical KC group and underwent a combination of accelerated corneal collagen cross-linking and topography-guided customized treatment with an excimer laser. RESULTS: The study included 1262 eyes (618 normal, 530 KC, and 114 FFKC) of 1262 patients. We observed that maximum decentration (MaxDec) was almost as good as maximum keratometry (Kmax) in detecting progressive KC. The area under the curve (AUC) was 0.95 for KC [95% confidence interval (CI): 0.93-0.96] and 0.84 for FFKC (95%CI: 0.79-0.88). Higher predictive accuracy was obtained using a model combining the spherical component, MaxDec, irregularity, and regular astigmatism in the center of the cornea (AUC: 0.97; sensitivity: 89%, and specificity: 96%). CONCLUSION: Decentration, Kmax, and posterior radii of curvatures from a 3.0-mm optical zone centered on the thinnest point of the cornea provide the highest accuracy with low reproducibility of Kmax.

LENNA (Learning Emotions Neural Network Assisted): An Empathic Chatbot Designed to Study the Simulation of Emotions in a Bot and Their Analysis in a Conversation

Currently, most chatbots are unable to detect the emotional state of the interlocutor and respond according to the interlocutor’s emotional state. Over the last few years, there has been growing interest in empathic chatbots. In other disciplines aside from artificial intelligence, e.g., in medicine, there is growing interest in the study and simulation of human emotions. However, there is a fundamental issue that is not commonly addressed, and it is the design of protocols for quantitatively evaluating an empathic chatbot by utilizing the analysis of the conversation between the bot and an interlocutor. This study is motivated by the aforementioned scenarios and by the lack of methods for assessing the performance of an empathic bot; thus, a chatbot with the ability to recognize the emotions of its interlocutor is needed. The main novelty of this study is the protocol with which it is possible to analyze the conversations between a chatbot and an interlocutor, regardless of whether the latter is a person or another chatbot. For this purpose, we have designed a minimally viable prototype of an empathic chatbot, named LENNA, for evaluating the usefulness of the proposed protocol. The proposed approach uses Shannon entropy to measure the changes in the emotional state experienced by the chatbot during a conversation, applying sentiment analysis techniques to the analysis of the conversation. Once the simulation experiments were performed, the conversations were analyzed by applying multivariate statistical methods and Fourier analysis. We show the usefulness of the proposed methodology for evaluating the emotional state of LENNA during conversations, which could be useful in the evaluation of other empathic chatbots.

Randomized Benchmarking as Convolution: Fourier Analysis of Gate Dependent Errors

We show that the Randomized Benchmarking (RB) protocol is a convolution amenable to Fourier space analysis. By adopting the mathematical framework of Fourier transforms of matrix-valued functions on groups established in recent work from Gowers and Hatami \cite{GH15}, we provide an alternative proof of Wallman's \cite{Wallman2018} and Proctor's \cite{Proctor17} bounds on the effect of gate-dependent noise on randomized benchmarking. We show explicitly that as long as our faulty gate-set is close to the targeted representation of the Clifford group, an RB sequence is described by the exponential decay of a process that has exactly two eigenvalues close to one and the rest close to zero. This framework also allows us to construct a gauge in which the average gate-set error is a depolarizing channel parameterized by the RB decay rates, as well as a gauge which maximizes the fidelity with respect to the ideal gate-set.