Characteristic Function Research Articles

Constrained optimal grouping of cloud application components

Cloud applications are built from a set of components often deployed as containers, which can be deployed individually on separate Virtual Machines (VMs) or grouped on a smaller set of VMs. Additionally, the application owner may have inhibition constraints regarding the co-location of components. Finding the best way to deploy an application means finding the best groups of components and the best VMs, and it is not trivial because of the complexity coming from the number of possible options. The problem can be mapped onto may known combinatorial problems as binpacking and knapsack formulations. However, these approaches often assume homogeneus resources and fail to incorporate the inhibition constraints. The main contribution of this paper are firstly a novel formulation of the grouping problem as constrained Coalition Structure Generation (CSG) problem, including the specification of the value function which fulfills the criteria of a Characteristic Function Game (CFG). The CSG problem aims to determine stable and disjoint groups of players collaborating to optimize the joint outcome of the game, and a CFG is a common representation of a CSG, where each group is assigned a value and where the value of the game is the sum of the groups’ contributions. Secondly, the Integer-Partition (IP) CSG algorithm has been modified and extended to handle constraints. The proposed approach is evaluated with the extended IP algorithm, and a novel exhaustive search algorithm establishing the optimum grouping for comparison. The evaluation shows that our approach with the modified algorithm evaluates on average significantly less combinations than the CSG state-of-the-art algorithm. The proposed approach is promising for optimized constrained Cloud application management as the modified IP algorithm can optimally solve constrained grouping problems of attainable sizes.

Forward Starting Option Pricing under Double Fractional Stochastic Volatilities and Jumps

This paper aims to provide an effective method for pricing forward starting options under the double fractional stochastic volatilities mixed-exponential jump-diffusion model. The value of a forward starting option is expressed in terms of the expectation of the forward characteristic function of log return. To obtain the forward characteristic function, we approximate the pricing model with a semimartingale by introducing two small perturbed parameters. Then, we rewrite the forward characteristic function as a conditional expectation of the proportion characteristic function which is expressed in terms of the solution to a classic PDE. With the affine structure of the approximate model, we obtain the solution to the PDE. Based on the derived forward characteristic function and the Fourier transform technique, we develop a pricing algorithm for forward starting options. For comparison, we also develop a simulation scheme for evaluating forward starting options. The numerical results demonstrate that the proposed pricing algorithm is effective. Exhaustive comparative experiments on eight models show that the effects of fractional Brownian motion, mixed-exponential jump, and the second volatility component on forward starting option prices are significant, and especially, the second fractional volatility is necessary to price accurately forward starting options under the framework of fractional Brownian motion.

Optimization of phosphorus wet acid extraction from sewage sludge ashes: Detailed process insight via multi-variate statistical techniques

To tackle the issue of phosphorus (P) supply, Sewage Sludge Ash (SSA) is a promising secondary source. The goal of this research is the optimization of the wet P extraction process in the view of providing valuable insights for the process scale-up. While most of the studies relied on the “one-variable-changed-at-a-time” approach, this work applied a statistical optimization model based on the Design of Experiments technique for investigating the influence of most relevant operating conditions of extraction process on Phosphorus Extraction Efficiency (PEE) with two types of SSA characterized by different levels of alkalinity. Experimental results highlighted the importance of ash characteristics, making some SSA not suitable for cost-effective phosphorus recovery due to the high acid dosage required in extraction process. Type of acid and contact time become significant factors only for Ca-rich ashes, especially when using H2SO4 as extracting agent. Optimal operating conditions (CH2SO4 = 1.3 N, L/S = 20, t = 2 h and CHCl = 2.0 N, L/S = 10, t = 2 h for Ash#1 and CH2SO4/HCl = 0.8 N, L/S = 10 for Ash#2) resulting in high PEE (80–94%) were identified for extraction performed with H2SO4 and HCl as a function of ash characteristics.

Global joint position regulation of a class of torque-driven robot manipulators within actuators prescribed safe operating torque–speed area

This paper addresses the joint position regulation of a class of n degrees of freedom torque-driven robot manipulators under a novel practical motivated control objective: Simultaneous Regulation & Prescribed Safe Operating Area (SR&PSOA). More specifically, torque–speed characteristic safe limit functions associated to each actuator are taking into account to ensure that besides of global joint positioning, the requested torque control inputs to robot actuators remain inside user prescribed safe operating torque–speed areas, so avoiding thermal and physical actuator damages. A static smooth nonlinear controller is proposed to achieve global position regulation under prescribed speed-depending bound torque input. Numerical simulations and experimental results are included to illustrate the effectiveness of the proposed controller.

Concealing Organic Neuromorphic Devices with Neuronal-Inspired Supported Lipid Bilayers.

Neurohybrid systems have gained large attention for their potential as in vitro and in vivo platform to interrogate and modulate the activity of cells and tissue within nervous system. In this scenario organic neuromorphic devices have been engineered as bioelectronic platforms to resemble characteristic neuronal functions. However, aiming to a functional communication with neuronal cells, material synthesis, and surface engineering can yet be exploited for optimizing bio-recognition processes at the neuromorphic-neuronal hybrid interface. In this work, artificial neuronal-inspired lipid bilayers have been assembled on an electrochemical neuromorphic organic device (ENODe) to resemble post-synaptic structural and functional features of living synapses. Here, synaptic conditioning has been achieved by introducing two neurotransmitter-mediated biochemical signals, to induce an irreversible change in the device conductance thus achieving Pavlovian associative learning. This new class of in vitro devices can be further exploited for assembling hybrid neuronal networks and potentially for in vivo integration within living neuronal tissues.

Estimation and comparison of Weibull-Normal distribution with some other probability models using Bayesian method of estimation

In statistical applications the Normal distribution is adjudged to be the best. Recent studies Terna (2017) using classical method indicated that Weibull-Normal distribution outperformed the Normal distribution. In this study we used the non-classical Bayesian method of estimation to estimate and compare the Weibull-Normal distribution with some other distributions including Normal and Gamma-Normal distributions. This study derived explicit expressions for basic statistical properties such as moments, moment generating function, the characteristic function, reliability analysis and the distribution of order statistics. It looks at estimation of confidence intervals for the parameters of the Weibull-Normal distribution and estimated the parameters of the new distribution using a non-classical approach for the purpose of theoretical comparisons. The two other distributions whose parameters were also estimated by using Bayesian estimation are the normal distribution and gamma distribution as well as the combination Gamma-Normal distribution. Based on the analyses and interpretations of the results obtained it was found that the parameters and other general properties of Normal distribution gives a better fit than other distributions. R-software was used; the models were written as an R code in R program using the rjags library, the distribution parameters were obtained from a Gibbs sampling of a Bayesian Fit for data set I and data set II. The criteria used in R for comparisons were the negative log-likelihood, AIC (Akaike information criterion), CAIC (Consistent Akaike Information Criterion) and BIC (Bayesian information Criterion).

Characters of [formula omitted] and vertex operators

In this paper, we present a vertex operator approach to construct and compute all complex irreducible characters of the general linear group GLn(Fq). Green's theory of GLn(Fq) is recovered and enhanced under the realization of the Grothendieck ring of representations RG=⨁n≥0R(GLn(Fq)) as two isomorphic Fock spaces associated to two infinite-dimensional F-equivariant Heisenberg Lie algebras hˆF‾ˆq and hˆF‾q, where F is the Frobenius automorphism of the algebraically closed field F‾q. Under this picture, the irreducible characters are realized by the Bernstein vertex operators for Schur functions, the characteristic functions of the conjugacy classes are realized by the vertex operators for the Hall-Littlewood functions, and the character table is completely given by matrix coefficients of vertex operators of these two types. One of the features of the current approach is a simpler identification of the Fock space RG as the Hall algebra of symmetric functions via vertex operator calculus, and another is that we are able to compute in general the character table, where Green's degree formula is demonstrated as an example.

Generalized Characteristic Function Loss for Crowd Analysis in the Frequency Domain.

Typical approaches that learn crowd density maps are limited to extracting the supervisory information from the loosely organized spatial information in the crowd dot/density maps. This paper tackles this challenge by performing the supervision in the frequency domain. More specifically, we devise a new loss function for crowd analysis called generalized characteristic function loss (GCFL). This loss carries out two steps: 1) transforming the spatial information in density or dot maps to the frequency domain; 2) calculating a loss value between their frequency contents. For step 1, we establish a series of theoretical fundaments by extending the definition of the characteristic function for probability distributions to density maps, as well as proving some vital properties of the extended characteristic function. After taking the characteristic function of the density map, its information in the frequency domain is well-organized and hierarchically distributed, while in the spatial domain it is loose-organized and dispersed everywhere. In step 2, we design a loss function that can fit the information organization in the frequency domain, allowing the exploitation of the well-organized frequency information for the supervision of crowd analysis tasks. The loss function can be adapted to various crowd analysis tasks through the specification of its window functions. In this paper, we demonstrate its power in three tasks: Crowd Counting, Crowd Localization and Noisy Crowd Counting. We show the advantages of our GCFL compared to other SOTA losses and its competitiveness to other SOTA methods by theoretical analysis and empirical results on benchmark datasets. Our codes are available at https://github.com/wbshu/Crowd_Counting_in_the_Frequency_Domain.

Area Vulnerability and Disparities in Therapy for Patients With Metastatic Renal Cell Carcinoma.

Area-level measures of sociodemographic disadvantage may be associated with racial and ethnic disparities with respect to receipt of treatment for metastatic renal cell carcinoma (mRCC) but have not been investigated previously, to our knowledge. To assess the association between area-level measures of social vulnerability and racial and ethnic disparities in the treatment of US Medicare beneficiaries with mRCC from 2015 through 2019. This retrospective cohort study included Medicare beneficiaries older than 65 years who were diagnosed with mRCC from January 2015 through December 2019 and were enrolled in fee-for-service Medicare Parts A, B, and D from 1 year before through 1 year after presumed diagnosis or until death. Data were analyzed from November 22, 2022, through January 26, 2024. Five different county-level measures of disadvantage and 4 zip code-level measures of vulnerability or deprivation and segregation were used to dichotomize whether an individual resided in the most vulnerable quartile according to each metric. Patient-level factors included age, race and ethnicity, sex, diagnosis year, comorbidities, frailty, Medicare and Medicaid dual enrollment eligibility, and Medicare Part D low-income subsidy (LIS). The main outcomes were receipt and type of systemic therapy (oral anticancer agent or immunotherapy from 2 months before to 1 year after diagnosis of mRCC) as a function of patient and area-level characteristics. Multivariable regression analyses were used to adjust for patient factors, and odds ratios (ORs) from logistic regression and relative risk ratios (RRRs) from multinomial logistic regression are reported. The sample included 15 407 patients (mean [SD] age, 75.6 [6.8] years), of whom 9360 (60.8%) were men; 6931 (45.0%), older than 75 years; 93 (0.6%), American Indian or Alaska Native; 257 (1.7%), Asian or Pacific Islander; 757 (4.9%), Hispanic; 1017 (6.6%), non-Hispanic Black; 12 966 (84.2%), non-Hispanic White; 121 (0.8%), other; and 196 (1.3%), unknown. Overall, 8317 patients (54.0%) received some type of systemic therapy. After adjusting for individual factors, no county or zip code-level measures of social vulnerability, deprivation, or segregation were associated with disparities in treatment. In contrast, patient-level factors, including female sex (OR, 0.78; 95% CI, 0.73-0.84) and LIS (OR, 0.48; 95% CI, 0.36-0.65), were associated with lack of treatment, with particularly limited access to immunotherapy for patients with LIS (RRR, 0.25; 95% CI, 0.14-0.43). Associations between individual-level factors and treatment in multivariable analysis were not mediated by the addition of area-level metrics. Disparities by race and ethnicity were consistently and only observed within the most vulnerable areas, as indicated by the top quartile of each vulnerability deprivation index. In this cohort study of older Medicare patients diagnosed with mRCC, individual-level demographics, including race and ethnicity, sex, and income, were associated with receipt of systemic therapy, whereas area-level measures were not. However, individual-level racial and ethnic disparities were largely limited to socially vulnerable areas, suggesting that efforts to improve racial and ethnic disparities may be most effective when targeted to socially vulnerable areas.

Towards the systematic reconnaissance of seismic signals from glaciers and ice sheets – Part 1: Event detection for cryoseismology

Abstract. Cryoseismology is a powerful toolset for progressing the understanding of the structure and dynamics of glaciers and ice sheets. It can enable the detection of hidden processes such as brittle fracture, basal sliding, transient hydrological processes, and calving. Addressing the challenge of detecting signals from many different processes, we present a novel approach for the semi-automated detection of events and event-like noise, which is well-suited for use as Part 1 of a workflow where unsupervised machine learning will be used as Part 2 (Latto et al., 2024) to facilitate the main reconnaissance of diverse detected event types. Implemented in the open-source and widely used ObsPy Python package, the multi-STA/LTA algorithm constructs a hybrid characteristic function from a set of short-term average (sta)–long-term average (lta) pairs (refer to Sect. 2 in the main text for an explanation of how uppercase and lowercase STA/sta and LTA/lta abbreviations are differentiated). We apply the algorithm to data from a seismic array deployed on the Whillans Ice Stream (WIS) in West Antarctica (austral summer 2010–2011) to form a “catch-all” catalogue of events and event-like noise. The new algorithm compares favorably with standard approaches, yielding a diversity of seismic events, including all previously identified stick-slip events (Pratt et al., 2014), teleseisms, and other noise-type signals. In terms of a catalogue overview, we investigate a partial association of seismicity with the tidal cycle and a slight association with ice temperature changes of the Antarctic summer. The new algorithm and workflow will assist in the comparison of different glacier environments using seismology, the identification of process change over time, and the targeting of possible subsequent high-resolution studies.

Not an immune cell, but they may act like one-cells with immune properties outside the immune system.

The cells presented in this work are not classified as cells that make up the immune system. They, however, present functions and molecules, which are characteristic of immune cells. These characteristic functions are, for example, sensing threat, performing phagocytosis, presentation of foreign antigens, cytokine release or enhancing immune memory. The enlisted immune response mechanisms are carried out by the possession of molecules such as Toll-like receptors, receptors for the Fc fragment of IgG, major histocompatibility complex class II molecules, costimulatory CD80/CD86 proteins and molecules needed for NLRP3 (NOD-like family pyrin domain containing 3) inflammasome activation. Thanks to these properties, the described nonimmune cells play an important role in the local immune response and support of the entire body in the fight against pathogens. They constitute the first line of defense of tissues and organs against pathogens and molecules recognized as harmful. The cells described in this article are particularly important in immunologically privileged places (e.g. the Bowman's capsule in the kidney), where "typical" immune cells normally do not have access. In this paper, we present immune-like functions and molecule suites of resident kidney cells (podocytes and mesangial cells), cochlear resident cells, fibrocytes and fibroblasts, as well as some stem cells (mesenchymal stem cells and umbilical cord Wharton's jelly-derived cells).

Inhibitory roles of Apolipoprotein E Christchurch astrocytes in curbing tau propagation using human pluripotent stem cell-derived models.

Genetic variants in the apolipoprotein E (APOE) gene affect the onset and progression of Alzheimer's disease (AD). The APOE Christchurch (APOE Ch) variant has been identified as the most prominent candidate for preventing the onset and progression of AD. In this study, we generated isogenic APOE3Ch/3Ch human induced pluripotent stem cells (iPSCs) from APOE3/3 healthy control female iPSCs and induced them into astrocytes. RNA expression analysis revealed the inherent resilience of APOE3Ch/3Ch astrocytes to induce a reactive state in response to inflammatory cytokines. Moreover, cytokine treatment changed astrocytic morphology with more complexity in APOE3/3 astrocytes, but not in APOE3Ch/3Ch astrocytes, indicating resilience of the rare variant to a reactive state. Interestingly, we observed robust morphological alterations containing more intricate processes when cocultured with iPSC-derived cortical neurons, in which APOE3Ch/3Ch astrocytes reduced complexity compared with APOE3/3 astrocytes. To assess the impacts of tau propagation effects, we next developed a sophisticated and sensitive assay utilizing cortical neurons derived from human iPSCs, previously generated from donors of both sexes. We showed that APOE3Ch/3Ch astrocytes effectively mitigated tau propagation within iPSC-derived neurons. This study provides important experimental evidence of the characteristic functions exhibited by APOE3Ch/3Ch astrocytes, thereby offering valuable insights for the advancement of novel clinical interventions in AD research.Significance Statement Alzheimer's disease (AD) is a degenerative disease that causes cognitive decline. Familial AD is a severe form caused by mutations in the PSEN1, PSEN2, or APP genes. One carrier of the PSEN1 mutation did not develop dementia. This carrier also had a rare variant of the APOE gene, the Christchurch variant. The APOE Christchurch variant may protect against familial AD. The mechanism of this protection is not fully understood. In the present study, we have successfully demonstrated that the APOE Christchurch variant suppresses the propagation of tau and exhibits a diminished capacity to convert native astrocytes into reactive astrocytes. These significant findings contribute novel insights to the field of the APOE gene and AD research.

Origin of Anomalously Large Depletion Zones in Like-Charged Colloid-Polyelectrolyte Mixtures.

Depletion zones in polyelectrolyte solutions in contact with like-charged flat surfaces are investigated. Using a coupled self-consistent field and Debye-Hückel approach, an explicit expression for the thickness δ of the depletion layer is derived. It is found that δ∼δ_{n}+cκ^{-1}, where δ_{n} is the depletion thickness at a neutral surface, c is a function of the electrostatic characteristics of the system, and κ^{-1} is the Debye length. It is argued that the theory still holds beyond the mean-field approximation, which is confirmed by quantitative agreement between our theoretical results and experiments.

Differential Games with Additive Payoffs

Differential games with additive payoffs are considered. A new approach to constructing the characteristic function for such games is defined. Properties of optimality principles such as the core and the Shapley value constructed by applying the new characteristic function are studied. The solutions obtained are demonstrated by means of an example.

Identification and estimation of panel semiparametric conditional heteroskedastic frontiers with dynamic inefficiency

We study a semiparametric panel stochastic frontier model with nonseparable unobserved heterogeneity, which allows for time-varying conditional heteroskedastic productivity components. It does not require distributional assumptions on random noise except conditional symmetry. We utilize conditional characteristic functions from Kotlarski’s Lemma to derive new moment conditions that yield the identification of the heteroskedastic variance parameters of inefficiency and random noise. Identification only requires a panel with three periods for serially correlated inefficiency. A nonparametric estimation procedure is also developed for the conditional variance of inefficiency, and its convergence rate is established. Monte Carlo simulation shows that the estimator is robust to misspecification of inefficiency distributions.

Stability properties of ultraholomorphic classes of Roumieu-type defined by weight matrices

We characterize several stability properties, such as inverse or composition closedness, for ultraholomorphic function classes of Roumieu type defined in terms of a weight matrix. In this way we transfer and extend known results from J. Siddiqi and M. Ider, from the weight sequence setting and in sectors not wider than a half-plane, to the weight matrix framework and for sectors in the Riemann surface of the logarithm with arbitrary opening. The key argument rests on the construction, under suitable hypotheses, of characteristic functions in these classes for unrestricted sectors. As a by-product, we obtain new stability results when the growth control in these classes is expressed in terms of a weight sequence, or of a weight function in the sense of Braun–Meise–Taylor.

New moment formulas for moments and characteristic function of the geometric distribution in terms of Apostol–Bernoulli polynomials and numbers

Although it is very easy to calculate the 1st moment and 2nd moment values of the geometric distribution with the methods available in existing books and other articles, it is quite difficult to calculate moment values larger than the 3rd order. Because in order to find these moment values, many higher order derivatives of the geometric series and convergence properties of the series are needed. The aim of this article is to find new formulas for characteristic function of the geometric random variable (with parameter p) in terms of the Apostol–Bernoulli polynomials and numbers, and the Stirling numbers. This characteristic function characterizes the geometric distribution. Using the Euler's identity, we give relations among this characteristic function, the Apostol–Bernoulli polynomials and numbers, and also trigonometric functions including and . A relations between the characteristic function and the moment generating function is also given. By using these relations, we derive new moments formulas in terms of the Apostol–Bernoulli polynomials and numbers. Moreover, we give some applications of our new formulas.

A matter of connection: the importance of habitat networks for endangered butterflies in anthropogenic landscapes

AbstractCities are expanding at fast rates across the world, representing one of the main drivers of biodiversity loss due to habitat replacement. Nonetheless, urban and peri-urban areas often feature green spaces that may offer opportunities to wildlife and even represent safe havens for endangered species. Nonetheless, the key drivers that shape wildlife responses to urban landscapes, and in turn their ability to persist within cities, are far from being fully understood. Here we focus on an ecologically specialized butterfly, the endemic Italian festoon Zerynthia cassandra, as a model to assess how endangered species may survive in highly modified urban landscapes. The relatively low mobility and high host plant specialization make Z. cassandra an excellent target for studies in urban ecology, as they make the species able to exploit small suitable patches while at the same time potentially sensitive to habitat fragmentation and loss due to urbanization and land reclamation. We thus first document the relatively widespread occurrence of potentially suitable sites within two highly modified landscapes of central and southern Italy, with 25 and 35% of sites actually occupied by Z. cassandra. By modeling the probability of butterfly occurrence as a function of environmental characteristics, we found that Z. cassandra is strongly influenced by functional connectivity among suitable sites in urban landscapes, as well as by the abundance of Aristolochia host plants, and by the availability of profitable land cover classes in the immediate surroundings of potential oviposition sites. Our results indicate not only that networks of urban and peri-urban green spaces may host populations of protected and endangered species, but that management should also focus on the urban matrix in order to provide connecting corridors, as key assets to guarantee species persistence in cities.

Photophysical image analysis: Unsupervised probabilistic thresholding for images from electron-multiplying charge-coupled devices.

We introduce the concept photophysical image analysis (PIA) and an associated pipeline for unsupervised probabilistic image thresholding for images recorded by electron-multiplying charge-coupled device (EMCCD) cameras. We base our approach on a closed-form analytic expression for the characteristic function (Fourier-transform of the probability mass function) for the image counts recorded in an EMCCD camera, which takes into account both stochasticity in the arrival of photons at the imaging camera and subsequent noise induced by the detection system of the camera. The only assumption in our method is that the background photon arrival to the imaging system is described by a stationary Poisson process (we make no assumption about the photon statistics for the signal). We estimate the background photon statistics parameter, λbg, from an image which contains both background and signal pixels by use of a novel truncated fit procedure with an automatically determined image count threshold. Prior to this, the camera noise model parameters are estimated using a calibration step. Utilizing the estimates for the camera parameters and λbg, we then introduce a probabilistic thresholding method, where, for the first time, the fraction of misclassified pixels can be determined a priori for a general image in an unsupervised way. We use synthetic images to validate our a priori estimates and to benchmark against the Otsu method, which is a popular unsupervised non-probabilistic image thresholding method (no a priori estimates for the error rates are provided). For completeness, we lastly present a simple heuristic general-purpose segmentation method based on the thresholding results, which we apply to segmentation of synthetic images and experimental images of fluorescent beads and lung cell nuclei. Our publicly available software opens up for fully automated, unsupervised, probabilistic photophysical image analysis.

Two results on the value distribution of meromorphic functions

Abstract In this article, we prove two results on the value distribution of meromorphic functions. Using the theorem of Yamanoi, the first result gives a precise estimation of the relationship between the characteristic function of a meromorphic function and its k k th derivative in a concise form. This result extends and improves some results of Shan, Singh, Gopalakrishna, Edrei, Weitsman, Yang, Wu and Wu, etc. The second result answers a conjecture posed by C. C. Yang. This conjecture turned to be false by a counter-example, but it will be true with an additional condition.