Exponential Diffusion Research Articles

Role of fluctuations in epidemic resurgence after a lockdown

Most popular statistical models in epidemic evolution focus on the dynamics of average relevant quantities and overlooks the role of small fluctuations on the model parameters. Models for Covid-19 are no exception. In this paper we show that the role of time-correlated fluctuations, far from being negligible, can in fact determine the spreading of an epidemic and, most importantly, the resurgence of the exponential diffusion in the presence of time-limited episodes in promiscuity behaviours. The results found in this work are not only relevant and specific for the Covid-19 epidemic but are more general and can be applied to other epidemics.

Parsimonious modeling of skeletal muscle perfusion: Connecting the stretched exponential and fractional Fickian diffusion.

To develop an anomalous (non-Gaussian) diffusion model for characterizing skeletal muscle perfusion using multi-b-value DWI. Fick's first law was extended for describing tissue perfusion as anomalous superdiffusion, which is non-Gaussian diffusion exhibiting greater particle spread than that of the Gaussian case. This was accomplished using a space-fractional derivative that gives rise to a power-law relationship between mean squared displacement and time, and produces a stretched exponential signal decay as a function of b-value. Numerical simulations were used to estimate parameter errors under in vivo conditions, and examine the effect of limited SNR and residual fat signal. Stretched exponential DWI parameters, α and , were measured in thigh muscles of 4 healthy volunteers at rest and following in-magnet exercise. These parameters were related to a stable distribution of jump-length probabilities and used to estimate microvascular volume fractions. Numerical simulations showed low dispersion in parameter estimates within 1.5% and 1%, and bias errors within 3% and 10%, for α and , respectively. Superdiffusion was observed in resting muscle, and to a greater degree following exercise. Resting microvascular volume fraction was between 0.0067 and 0.0139 and increased between 2.2-fold and 4.7-fold following exercise. This model captures superdiffusive molecular motions consistent with perfusion, using a parsimonious representation of the DWI signal, providing approximations of microvascular volume fraction comparable with histological estimates. This signal model demonstrates low parameter-estimation errors, and therefore holds potential for a wide range of applications in skeletal muscle and elsewhere in the body.

The utility of ADC parameters in the diagnosis of clinically significant prostate cancer by 3.0-Tesla diffusion-weighted magnetic resonance imaging.

PurposeThis study has focused on investigating the relationship between the exponential apparent diffusion coefficient (exp-ADC), selective apparent diffusion coefficient (sel-ADC) values, the ADC ratio (ADCr), and prostate cancer aggressiveness with transrectal ultrasound-guided prostate biopsy in patients with prostate cancer.Material and methodsAll patients underwent a multiparametric magnetic resonance imaging (mpMRI) including tri-planar T2-weighted (T2W), dynamic contrast-enhanced (DCE), diffusion-weighted sequences using a 3.0-Tesla MR scanner (Skyra, Siemens Medical Systems, Germany) with a dedicated 18-channel body coil and a spine coil underneath the pelvis, with the patient in the supine position. Exp-ADC, sel-ADC, and ADCr of defined lesions were evaluated using region-of-interest-based measurements. Exp-ADC, sel-ADC, and ADCr were correlated with the Gleason score obtained through transrectal ultrasound-guided biopsy.ResultsPatients were divided into 2 groups. Group I is Gleason score ≥ 3 + 4, group II is Gleason score = 6. Sel-ADC and exp-ADC were statistically significant between 2 groups (0.014 and 0.012, respectively). However, the ADCr difference between nonclinical significant prostate cancer from clinically significant prostate cancer was not significant (p = 0.09).ConclusionsThis study is the first to evaluate exp-ADC and sel-ADC values of prostate carcinoma with ADCr. One limitation of this study might be the limited number of patients. Exp-ADC and sel-ADC values in prostate MRI imaging improved the specificity, accuracy, and area under the curve (AUC) for detecting clinically relevant prostate carcinoma. Adding exp-ADC and sel-ADC values to ADCr can be used to increase the diagnostic accuracy of DWI.

Pricing Bitcoin under Double Exponential Jump-Diffusion Model with Asymmetric Jumps Stochastic Volatility

The objective of this study is, to show the importance of incorporating jumps in both returns and volatility dynamics for Bitcoin. For that purpose, we introduce the Double Exponential Jump-Diffusion model with Stochastic Volatility (DEJDSVJ) that contains asymmetric jumps. The use of the Markov Chain Monte Carlo methods for estimation has proved the meaningful presence of jumps in Bitcoin price and volatility. Moreover, based on the Bitcoin options market, a comparison between the underlying model, the Double Exponential Jump Diffusion model (DEJD) with Stochastic Volatility (no Jumps) and the Stochastic Volatility (SV) shows the goodness of the DEJDSVJ model’s calibration over others for pricing Bitcoin options.

Automatic Transportation Mode Recognition on Smartphone Data Based on Deep Neural Networks.

In the last few years, with the exponential diffusion of smartphones, services for turn-by-turn navigation have seen a surge in popularity. Current solutions available in the market allow the user to select via an interface the desired transportation mode, for which an optimal route is then computed. Automatically recognizing the transportation system that the user is travelling by allows to dynamically control, and consequently update, the route proposed to the user. Such a dynamic approach is an enabling technology for multi-modal transportation planners, in which the optimal path and its associated transportation solutions are updated in real-time based on data coming from (i) distributed sensors (e.g., smart traffic lights, road congestion sensors, etc.); (ii) service providers (e.g., car-sharing availability, bus waiting time, etc.); and (iii) the user’s own device, in compliance with the development of smart cities envisaged by the 5G architecture. In this paper, we present a series of Machine Learning approaches for real-time Transportation Mode Recognition and we report their performance difference in our field tests. Several Machine Learning-based classifiers, including Deep Neural Networks, built on both statistical feature extraction and raw data analysis are presented and compared in this paper; the result analysis also highlights which features are proven to be the most informative ones for the classification.

A One‐Dimensional Model for Turbulent Mixing in the Benthic Biolayer of Stream and Coastal Sediments

AbstractIn this paper, we develop and validate a rigorous modeling framework, based on Duhamel's Theorem, for the unsteady one‐dimensional vertical transport of a solute across a flat sediment‐water interface (SWI) and through the benthic biolayer of a turbulent stream. The modeling framework is novel in capturing the two‐way coupling between evolving solute concentrations above and below the SWI and in allowing for a depth‐varying diffusivity. Three diffusivity profiles within the sediment (constant, exponentially decaying, and a hybrid model) are evaluated against an extensive set of previously published laboratory measurements of turbulent mass transfer across the SWI. The exponential diffusivity profile best represents experimental observations and its reference diffusivity scales with the permeability Reynolds number, a dimensionless measure of turbulence at the SWI. The depth over which turbulence‐enhanced diffusivity decays is of the order of centimeters and comparable to the thickness of the benthic biolayer. Thus, turbulent mixing across the SWI may serve as a universal transport mechanism, supplying the nutrient and energy fluxes needed to sustain microbial growth, and nutrient processing, in the benthic biolayer of stream and coastal sediments.

A valuable MRI examination method for prostate cancer screening.

To investigate the value of the 1.5T magnetic resonance imaging (MRI) apparent diffusion coefficient (ADC) and the prostate imaging reporting and data system (PI-RADS) score in prostate cancer (PCa) screening.Forty PCa patients diagnosed by pathology from December 2014 to September 2018 were recruited as the PCa group; 60 patients with benign prostatic hyperplasia (BPH) were recruited as the benign group. Patients from both groups underwent 1.5T MRI scanning. The prostate ADC values, exponential apparent diffusion coefficient (eADC) values, and PI-RADS scores of patients from the 2 groups were compared. The different methods for PCa diagnosis were compared.The ADC values of patients in the PCa group were significantly lower than those in the benign group, whereas the eADC values of patients were significantly higher than those in the benign group, with statistically significant differences (P < .05). The differences in the PI-RADS scores of patients from the 2 groups were statistically significant (P < .05). Receiver Operating Characteristic (ROC) curve results showed that the ADC value combined with the PI-RADS score was superior to the ADC value or the PI-RADS score alone in sensitivity, specificity, and Youden index for PCa diagnosis. By comparing the area under the curve (AUC) of each ROC curve from the different diagnostic methods, the combination of ADC value and PI-RADS score showed the largest area.The ADC value from 1.5T MRI combined with the PI-RADS score could be used as the standard for PCa screening, which would effectively improve screening for PCa and be valuable for clinical applications.

Common model to approximate the time-variant behaviour of air humidity-change influence on some fundamental standards of precision electromagnetic measurement

In this work, a mathematical model originally developed for describing the dependence of Zener voltage output on air humidity is intended to be generalized by applying it to inductance and resistance measurements. It is shown that the influence of varying humidity behaviors, through the exponential decay diffusion of water vapor followed by corresponding variations of electromagnetic features, as a macro-relaxation process inside the air interaction space of measured object. The relaxation time constant of this process, ranging from minutes to weeks, is determined by the sealing conditions. Results of experimental studies on air humidity-change influence on ac self-inductance, dc mutual inductance and dc resistance measurements at NIM agree well with the theoretical analyses using this model. So far, the experiments make this model more suitable for main areas of electromagnetic measurement: using the model and tracking humidity data, the time-variant effect can be approximately compensated.

Chaotic dynamics of a non-Hermitian kicked particle

We investigate both the classical and quantum dynamics of a kicked particle with symmetry. In chaotic situation, the mean energy of the real parts of momentum linearly increases with time, and that of the imaginary momentum exponentially increases. There exists a breakdown time for chaotic diffusion, which is obtained both analytically and numerically. The quantum diffusion of this non-Hermitian system follows the classically chaotic diffusion of Hermitian case during the Ehrenfest time, after which it is completely suppressed. Interestingly, the Ehrenfest time decreases with the decrease of effective Planck constant or the increase of the strength of the non-Hermitian kicking potential. The exponential growth of the quantum out-of-time-order correlators (OTOC) during the initially short time interval characterizes the feature of the exponential diffusion of imaginary trajectories. The long time behavior of OTOC reflects the dynamical localization of quantum diffusion. The dynamical behavior of inverse participation ratio can quantify the symmetry breaking, for which the rule of the phase transition points is numerically obtained.

Chaotic dynamics of complex trajectory and its quantum signature* *Project partially supported by the National Natural Science Foundation of China (Grant Nos. 12065009, 11804130, and 11805165) and Zhejiang Provincial Nature Science Foundation, China (Grant No. LY20A050001).

We investigate both the quantum and classical dynamics of a non-Hermitian system via a kicked rotor model with symmetry. For the quantum dynamics, both the mean momentum and mean square of momentum exhibit the staircase growth with time when the system parameter is in the neighborhood of the symmetry breaking point. If the system parameter is much larger than the symmetry breaking point, the accelerator mode results in the directed spreading of the wavepackets as well as the ballistic diffusion in momentum space. For the classical dynamics, the non-Hermitian kicking potential leads to the exponentially-fast increase of classical complex trajectories. As a consequence, the imaginary part of the trajectories exponentially diffuses with time, while the real part exhibits the normal diffusion. Our analytical prediction of the exponential diffusion of imaginary momentum and its breakdown time is in good agreement with numerical results. The quantum signature of the chaotic diffusion of the complex trajectories is reflected by the dynamics of the out-of-time-order correlators (OTOC). In the semiclassical regime, the rate of the exponential increase of the OTOC is equal to that of the exponential diffusion of the complex trajectories.

Symmetry properties of conservation laws for nonlinear Fokker-Planck equation describing cell population growth

Symmetry properties of conservation laws of the (2+1)-dimensional nonlinear Fokker-Planck equation describing the growing cell populations are studied. Firstly, a complete symmetry classification is performed with respect to an equivalence transformation. A two-dimensional optimal system of Lie subalgebras is constructed and used to transform the equations into ordinary differential equations. Secondly, all nontrivial conservation laws are determined via multiplier method and their symmetry properties including symmetry homogeneity and symmetry invariance are investigated in detail. Finally, the Fokker-Planck equation with exponential diffusion is further studied where some invariant solutions and all nontrivial conservation laws are found. In particular, a power series solution is constructed and shown to converge to certain invariant solutions by choosing proper parameters. Moreover, the symmetry invariant conservation laws are transformed into the conservation laws or first integrals of the reduced equations. Consequently, double reductions are performed and some exact solutions are found.

COVID-19 Pandemic in the Italian Population: Validation of a Post-Traumatic Stress Disorder Questionnaire and Prevalence of PTSD Symptomatology.

Since December 2019, the COVID-19 pandemic has attracted worldwide attention for its rapid and exponential diffusion. The long-term psychological impact, of both the spread of the virus and the restrictive policies adopted to counteract it, remains uncertain. However, recent studies reported a high level of psychological distress and Post-Traumatic Stress Disorder (PTSD) symptoms. The purpose of this study is to assess the psychometric properties of a new questionnaire, to evaluate PTSD risk related to the COVID-19 emergency. A total of Italian people completed a web-based cross-sectional survey broadcasted through different social-media. Demographic data and some psychological dimensions, such as general distress and sleep disturbance, were collected. A new self-report questionnaire (COVID-19-PTSD), consisting of 19 items, was developed starting from the PTSD Check List for DSM-5 (PCL-5) questionnaire, and it was administered in order to analyze its psychometric properties. The results highlighted the adequate psychometric properties of the COVID-19-PTSD questionnaire. The confirmatory factor analysis indicated that a seven-factor model (Intrusion, Avoidance, Negative Affect, Anhedonia, Dysphoric arousal, Anxious arousal and Externalizing behavior) best fits the data. Significant correlations were found among COVID-19-PTSD scores, general distress and sleep disturbance. A high percentage of PTSD symptomatology (29.5%) was found in the Italian population. COVID-19-PTSD appears to be effective in evaluating the specific stress symptoms related to the COVID-19 pandemic in the Italian population. These results are relevant from a clinical point of view because they suggest that the COVID-19 pandemic could be considered as a traumatic event. Psychological interventions to counteract short- and long-term psychopathological effects, consequent to the COVID-19 pandemic, appear to be necessary.

Option pricing on sesame price using jump diffusion models

In this paper, we aim at developing a model for option pricing to reduce the risks associated with Ethiopian sesame price fluctuations. The White Humera Gondar Sesame Grade 3 (WHGS3) price, which is recorded from 5 November 2010 to 30 March 2018 at Ethiopia Commodity Exchange (ECX) market, is used to analyze the price fluctuation. The nature of log-returns of the price is asymmetric (positively skewed) and exhibits high kurtosis. We used jump diffusion models for modeling and option pricing of sesame price. The method of maximum likelihood is applied to estimate the parameters of the models. We used the Root Mean Square Error (RMSE) to test the goodness of fitting for the two models to the data. This test indicates that the models fit the data well. The techniques of analytical and Monte Carlo simulation are used to find the call option pricing of WHGS3 sesame price. From the results, we concluded that Double Exponential Jump Diffusion (DEJD) model is more efficient than Merton’s model for modeling and option pricing of this sesame price.

Codifying Memories through Film

Abstract Before the exponential diffusion of modern video broadcasting media, the history of forced migrations within Africa was mainly transmitted through the spread of individual and collective memories. Filming, instead, agglomerates memories and images by producing new overarching and often convincing interpretations of the past. This article describes how and why a documentary video on slavery in the Indian Ocean was produced and the reasons behind its narrative form. Stemming from the urge of people regarded as descendants of slaves to have their ancestral dances documented as proof of their origins, this documentary is the result of a long-range ethnographic encounter spanning time and space from the Juba River in Somalia to Malawi and the Niasa region of Mozambique. It was only audiovisual equipment like video cameras and computers that made such an amazing encounter possible.

The value of DWI in predicting the response to synchronous radiochemotherapy for advanced cervical carcinoma: comparison among three mathematical models

BackgroundDiffusion weighted imaging(DWI) mode mainly includes intravoxel incoherent motion (IVIM), stretched exponential model (SEM) and Gaussian diffusion model, but it is still unclear which mode is the most valuable in predicting the response to radiochemotherapy for cervical cancer. This study aims to compare the values of three mathematical models in predicting the response to synchronous radiochemotherapy for cervical cancer.MethodsEighty-four patients with cervical cancer were enrolled into this study. They underwent DWI examination by using 12 b-values prior to treatment. The imaging parameters were calculated on the basis of IVIM, SEM and Gaussian diffusion models respectively. The imaging parameters derived from three mathematical modes were compared between responders and non-responders groups. The repeatability of each imaging parameter was assessed.ResultsThe ADC, D or DDC value was lower in responders than in non-responders groups (P = 0.03, 0.02, 0.01). The α value was higher in responders group than in non-responders group (P = 0.03). DDC had the largest area under curves (AUC) (=0.948) in predicting the response to treatment. The imaging parameters derived from SEM had better repeatability (CCC for DDC and α were 0.969 and 0.924 respectively) than that derived from other exponential models.ConclusionThree exponential modes of DWI are useful for predicting the response to radiochemotherapy for cervical cancer, and SEM may be used as a potential optimal model for predicting treatment effect.

Коронавирус в регионах России: особенности и последствия распространения

Russia and the world are experiencing a pandemic that is unprecedented in modern history in terms of the number of cases and socio-economic consequences. The article discusses the features of the statistical accounting of morbidity and mortality and how much they could affect the available estimates. The authors believe that the fixed incidence of the population obeys the laws of the distribution of innovations and depends on the structure and interaction within regional communities. According to the above calculations, if current conditions remain, the maximum number of infections can exceed 160 thousand people, and the end of the epidemic should be expected no earlier than mid-June. We are now at a stage of exponential growth and diffusion across the country. In general, in Russia, the closure and bankruptcy of 50-60% of firms in 2020, according to the most pessimistic scenario, is fraught with a fall in GDP by 3-10% for the year.

NIMG-55. TO ASSESS THE UTILITY OF ADVANCED QUANTITATIVE DIFFUSION MRI DERIVED FROM MULTI B VALUE ACQUISITIONS IN THE ASSESSMENT OF TREATMENT RESPONSE, USING A SPATIALLY-INDEPENDENT APPROACH

Abstract PURPOSE To assess the utility of advanced diffusion MRI derived from multi b value acquisitions in the assessment of treatment response, using a spatially-independent approach. METHOD AND MATERIALS 13 GBM patients were enrolled into our multicentre study. All patients completed RT with TMZ. Imaging was performed pre-RT and mid RT. The MRI protocol included a ‘low’ b value acquisition (b= 0s/mm, 50s/mm, 150s/mm, 200s/mm, 500s/mm, 1000s/mm) from which monoexponential diffusion indices ADC and biexponential indices, IVIM parameters D*, D and f were calculated. A ‘high b value’ acquisition (b=0 s/mm, 500s/mm, 1000s/mm, 1500s/mm, 2000s/mm, 2500s/mm, 3000s/mm, 3500s/mm, 4000s/mm) was acquired to allow stretched exponential diffusion indices, DDC and alpha to be derived. FLAIR sequences were used to define ROI and clinical assessment of mid-treatment and end-treatment response using RANO criteria. Histograms were generated from voxels located within manually segmented ROIs defined by increased signal on T2 FLAIR images. Changes in histogram percentile profiles were evaluated across the two timepoints and compared with RANO assessment at the mid treatment and end treatment timepoints. RESULTS Following completion of treatment, 5 patients had PD, 4 SD and 4 CR. Patients with PD showed a histogram shift to the left across all diffusion models, in keeping with increasing diffusion restriction and implying increased cellularity. Patients with SD or CR showed little or no shift in the histogram. DDC and f are the most predictive of progression against RANO assessment, and appear superior to routine ADC. Reduction in 75th centile (f) and 95th centile (DDC) are the most sensitive histogram metrics for predicting early progressive disease. CONCLUSION Results suggest association between early changes in specific diffusion components and subsequent treatment response. Spatially-independent diffusion parameter comparisons provide unbiased sampling of tumour heterogeneity and abrogate the confound of voxel-to-voxel misregistration due to tumour growth/shrinkage.

Predict the Shipment Forecast using Time-Series Data in Machine Learning

In the point of large big data and massive increase the rate of time series data flow in the upcoming market program business, mining of related data and real time data[1] are been briefly explained. This paper proposes predicted the value of the trader marketing when we reach the expected the value and increase the rate of accuracy. For this purpose we can use the time series algorithm in machine learning and gets regular item sets by using the corresponding of Map reduce [2], which consumes less space and will not increase the time overhead. The usage of CPU is improved by using the thread calling algorithm and batch algorithm, it meets deep business opportunities and requirement processing or feature model based on the requirements of traders. Thus our results indicates that the model not only explained the time series data stream[4],it also helps traders to get to a confirmation that they can achieve data quickly and achieve accuracy trade off's. This paper proposes a new demand forecasting model which is an extension of the traditional exponential diffusion models [5]. We examined the forecasting performance of the models just after the release of the item when the small number of model calibration data is available. This paper shows that the model which we proposed has the thing of enabling early decision making and best performance

Nipple‐sparing mastectomy combined with endoscopic immediate reconstruction via axillary incision for breast cancer: A preliminary experience of an innovative technique

Nipple-sparing mastectomy (NSM) has known an exponential diffusion worldwide for prophilaxis and therapeutic mastectomies in selected candidates, being oncologically safe and improving reconstructive outcomes and patients' satisfaction. The two most common used skin incisions are the radial and inframammary fold ones, which represent an imperfect aesthetic solution. The aim of this work was to give insights on our surgical technique, which allows to perform the NSM, node surgery, and endoscopic direct-to-implant reconstruction using a cosmetic axillary incision. Between June 2016 and January 2019, 7 consecutive patients underwent NSM, lymph node surgery and endoscopic direct-to-implant reconstruction using a small cosmetic axillary incision for breast cancer treatment in a single Institution. An operative rigid endoscope with working channel (Richard Wolf) was used to dissect the entire submuscular-subfascial pocket. The mean age of the patients was 42.8years old (range: 36-49years). The evaluation methods were clinical and photography-based assessments, as well as the BREAST-Q which was used to quantify patient satisfaction. The average follow-up time was 9months (range 3-22months). Tumor-free margins were obtained in all cases. No tumor recurrence or metastasis occurred during follow-up. No major complications were experienced. There were no cases of malposition, wrinkling, or rippling. All patients were satisfied with their esthetic results, especially the absence of visible scars. From our preliminary experience, NSM combined with endoscopic immediate reconstruction via axillary incision for breast cancer treatment seems to be a promising new procedure in cup A and B breasts alternative to the conventional techniques, as it allowed to have safe and pleasant aesthetic and oncologic outcomes.

Value and related factors of preoperative diagnosis of extramural vascular invasion of rectal cancer by 3.0T magnetic resonance imaging

Objective: To evaluate the value of preoperative diagnosis of extramural vascular invasion (EMVI) of rectal cancer with 3.0T high-resolution magnetic resonance imaging (MRI) and the MRI-related factors of EMVI in rectal cancer. Methods: The clinical and imaging data of 40 patients with rectal cancer were retrospectively analyzed. The postoperative pathological diagnosis was used as the gold standard to evaluate the diagnostic efficacy of preoperative diagnosis of EMVI of rectal cancer by high-resolution MRI, and to analyze the relationship between the EMVI and clinical and MRI features. Results: Of the 40 patients, 19 cases were diagnosed as positive EMVI and 21 were negative by MRI. Pathological diagnosis of EMVI was positive in 10 cases and negative in 30 cases. The sensitivity, specificity and accuracy of MRI in the diagnosis of EMVI were 100%, 70.0% and 77.5%, respectively. Preoperative MRI and postoperative pathology were moderately consistent in the diagnosis of EMVI in rectal cancer (Kappa=0.538, P<0.001). Pathological EMVI positivity were related to tumor size under MRI examination (P=0.028), degree of differentiation (P<0.001), depth of invasion (P=0.002), lymph node metastasis (P=0.001), liver metastasis (P=0.011), tumor apparent diffusion coefficient (ADC) value (P=0.010) and exponential apparent diffusion coefficient (eADC) value (P=0.003). It also related to extramural nerve invasion by pathological examination (P=0.005). Conclusion: According to the EMVI imaging score of rectal cancer, preoperative MRI has a high value in the diagnosis of EMVI of rectal cancer.