text:
# Variables and Symbols¶

There is a convention on consistent variable names throughout the library:

List of used Variables and Parameters
variable description
tz timezone
latitude latitude
longitude longitude
dni_extra direct normal irradiance at top of atmosphere (extraterrestrial)
aoi angle of incidence between $$90\deg$$ and $$90\deg$$
aoi_projection cos(aoi)
airmass airmass
airmass_relative relative airmass
airmass_absolute absolute airmass
poa_ground_diffuse in plane ground reflected irradiation
poa_diffuse total diffuse irradiation in plane. sum of ground and sky diffuse.
poa_global global irradiation in plane. sum of diffuse and beam projection.
poa_sky_diffuse diffuse irradiation in plane from scattered light in the atmosphere (without ground reflected irradiation)
surface_tilt tilt angle of the surface
surface_azimuth azimuth angle of the surface
solar_zenith zenith angle of the sun in degrees
apparent_zenith refraction-corrected solar zenith angle in degrees
solar_azimuth azimuth angle of the sun in degrees East of North
temp_cell temperature of the cell
temp_module temperature of the module
temp_air temperature of the air
temp_dew dewpoint temperature
relative_humidity relative humidity
v_mp, i_mp, p_mp module voltage, current, power at the maximum power point
v_oc open circuit module voltage
i_sc short circuit module current
i_x, i_xx Sandia Array Performance Model IV curve parameters
photocurrent photocurrent
saturation_current diode saturation current
resistance_series series resistance
resistance_shunt shunt resistance
transposition_factor the gain ratio of the radiation on inclined plane to global horizontal irradiation: $$\frac{poa\_global}{ghi}$$
pdc0 nameplate DC rating
pdc, dc dc power
gamma_pdc module temperature coefficient. Typically in units of 1/C.
pac, ac ac powe.
eta_inv inverter efficiency
eta_inv_ref reference inverter efficiency
eta_inv_nom nominal inverter efficiency

For a definition and further explanation on the variables, common symbols and units refer to the following sources:

Note

These further references might not use the same terminology as pvlib. But the physical process referred to is the same.

format: plain


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### Recent Submissions

• #### Uniting Heterogeneity, Inductiveness, and Efficiency for Graph Representation Learning

(IEEE Transactions on Knowledge and Data Engineering, IEEE, 2021-07-27) [Article]
Recently, bearing the message passing paradigm, graph neural networks(GNNs) have greatly advanced the performance of node representation learning on graphs. However, a majority class of GNNs are only designed for homogeneous graphs, leading to inferior adaptivity to the more informative heterogeneous graphs with various types of nodes and edges. Also, despite the necessity of inductively producing representations for completely new nodes (e.g., in streaming scenarios), few heterogeneous GNNs can bypass the transductive learning scheme where all nodes must be known during training. Furthermore, the training efficiency of most heterogeneous GNNs has been hindered by their sophisticated designs for extracting the semantics associated with each meta path or relation. In this paper, we propose a wide and deep message passing network (WIDEN) to cope with the aforementioned problems about heterogeneity, inductiveness, and efficiency that are rarely investigated together in graph representation learning. In WIDEN, we propose a novel inductive, meta path-free message passing scheme that packs up heterogeneous node features with their associated edges from both low- and high-order neighbor nodes. To further improve the training efficiency, we innovatively present an active down-sampling strategy that drops unimportant neighbor nodes to facilitate faster information propagation.
• #### All Screen-Printed, Polymer-Nanowire Based Foldable Electronics for mm-Wave Applications

(Advanced Materials Technologies, Wiley, 2021-07-26) [Article]
With the surge in devices for Internet of Things (IoT) applications, there is great interest in flexible electronics to be mass manufactured at lower costs. Screen-printing is well-known for mass manufacturing, however, this method has mostly focused on printing metallic patterns. Rare efforts have been devoted to print substrates for high frequency (mm-wave) electronics, which requires low dielectric loss to ensure a decent system efficiency. This paper presents a novel screen-printable composite ink comprising of acrylonitrile-butadiene-styrene and ceramic particles, through which, dielectric substrates with various thicknesses (down to few microns), lateral dimensions, and relative permittivities can be printed. A low dielectric loss of 0.0063 at 28 GHz (fifth generation (5G) communication band) makes the substrates suitable for mm-wave electronics. A custom silver nanowires based screen-printable ink is utilized for metallic printing to provide high conductivity (3.4 × 106 S m-1) and stable electrical response under bent or folded conditions. As a proof of concept for fully printed mm-wave electronics, a flexible quasi-Yagi antenna operating at 5G band (26.5–29.5 GHz) is demonstrated that exhibits decent performance in flat as well as bent conditions, confirming the suitability of the material system and printing processes for mass production of IoT and wearable electronics.
• #### Landslide size matters: A new data-driven, spatial prototype

(Engineering Geology, Elsevier BV, 2021-07-24) [Article]
The standard definition of landslide hazard requires the estimation of where, when (or how frequently) and how large a given landslide event may be. The geoscientific community involved in statistical models has addressed the component pertaining to how large a landslide event may be by introducing the concept of landslide-event magnitude scale. This scale, which depends on the planimetric area of the given population of landslides, in analogy to the earthquake magnitude, has been expressed with a single value per landslide event. As a result, the geographic or spatially-distributed estimation of how large a population of landslide may be when considered at the slope scale, has been disregarded in statistically-based landslide hazard studies. Conversely, the estimation of the landslide extent has been commonly part of physically-based applications, though their implementation is often limited to very small regions. In this work, we initially present a review of methods developed for landslide hazard assessment since its first conception decades ago. Subsequently, we introduce for the first time a statistically-based model able to estimate the planimetric area of landslides aggregated per slope units. More specifically, we implemented a Bayesian version of a Generalized Additive Model where the maximum landslide size per slope unit and the sum of all landslide sizes per slope unit are predicted via a Log-Gaussian model. These “max” and “sum” models capture the spatial distribution of (aggregated) landslide sizes. We tested these models on a global dataset expressing the distribution of co-seismic landslides due to 24 earthquakes across the globe. The two models we present are both evaluated on a suite of performance diagnostics that suggest our models suitably predict the aggregated landslide extent per slope unit. In addition to a complex procedure involving variable selection and a spatial uncertainty estimation, we built our model over slopes where landslides triggered in response to seismic shaking, and simulated the expected failing surface over slopes where the landslides did not occur in the past. What we achieved is the first statistically-based model in the literature able to provide information about the extent of the failed surface across a given landscape. This information is vital in landslide hazard studies and should be combined with the estimation of landslide occurrence locations. This could ensure that governmental and territorial agencies have a complete probabilistic overview of how a population of landslides could behave in response to a specific trigger. The predictive models we present are currently valid only for the 25 cases we tested. Statistically estimating landslide extents is still at its infancy stage. Many more applications should be successfully validated before considering such models in an operational way. For instance, the validity of our models should still be verified at the regional or catchment scale, as much as it needs to be tested for different landslide types and triggers. However, we envision that this new spatial predictive paradigm could be a breakthrough in the literature and, in time, could even become part of official landslide risk assessment protocols.
• #### Aerial Swarms: Recent Applications and Challenges

(Current Robotics Reports, 2021-07-23) [Article]
Purpose of Review Currently, there is a large body of research on multi-agent systems addressing their different system theoretic aspects. Aerial swarms as one type of multi-agent robotic systems have recently gained huge interest due to their potential applications. However, aerial robot groups are complex multi-disciplinary systems and usually research works focus on specific system aspects for particular applications. The purpose of this review is to provide an overview of the main motivating applications that drive the majority of research works in this field, and summarize fundamental and common algorithmic components required for their development. Recent Findings Most system demonstrations of current aerial swarms are based on simulations, some have shown experiments using few 10 s of robots in controlled indoor environment, and limited number of works have reported outdoor experiments with small number of autonomous aerial vehicles. This indicates scalability issues of current swarm systems in real world environments. This is mainly due to the limited confidence on the individual robot’s localization, swarm-level relative localization, and the rate of exchanged information between the robots that is required for planning safe coordinated motions. Summary This paper summarizes the main motivating aerial swarm applications and the associated research works. In addition, the main research findings of the core elements of any aerial swarm system, state estimation and mission planning, are also presented. Finally, this paper presents a proposed abstraction of an aerial swarm system architecture that can help developers understand the main required modules of such systems.
• #### Atomistic origin of compositional pulling effect in wurtzite (B, Al, In)xGa1−xN: A first-principles study

(Journal of Applied Physics, AIP Publishing, 2021-07-21) [Article]
Some fluctuations in composition are commonly observed in epitaxial-grown III-V multinary alloys. These fluctuations are attributed to compositional pulling effects, and an insight into their atomistic origin is necessary to improve current epitaxial growth techniques. In addition, the crystallinity of III-V multinary alloys varies widely depending on the constituent atoms. Using first-principles calculations, we then investigated different geometric configurations of gallium nitride (GaN)-based ternary alloy, X0.125Ga0.875N where X is the minority atom which is boron (B), aluminum (Al), or indium (In). The minority atoms are presented as two atoms in the simulation cell, and the energetics of five geometric configurations are analyzed to estimate the most stable configuration. For the B0.125Ga0.875N alloy, the most stable configuration is the one where the minority atoms occupy gallium (Ga) sites in a collinear orientation along the c-axis. On the contrary, the configurations along the in-plane direction result in a higher energy state. In0.125Ga0.875N and Al0.125Ga0.875N also show the same trend with a small relative energy difference. These preferential sites of minority atoms are consistent with composition pulling effects in wurtzite nitride phases. Moreover, the degree of crystallinity for wurtzite nitride alloys can be well described by the order of calculated relative energy.
• #### Re-infection with different SARS-CoV-2 clade and prolonged viral shedding in a patient with hematopoietic stem cell transplantation: SARS-CoV-2 Re-infection with different clade.

(International journal of infectious diseases : IJID : official publication of the International Society for Infectious Diseases, Elsevier BV, 2021-07-21) [Article]
Immunocompromised patients who have SARS-CoV-2 infection pose many clinical and public health challenges. We describe a patient with hematopoietic stem cell transplantation and lymphoma with protracted illness requiring 3 consecutive hospital admissions. Whole genome sequencing confirmed two different SARS-CoV-2 clades. Clinical management issues, and unanswered questions arising are discussed.
• #### CANITA: Faster Rates for Distributed Convex Optimization with Communication Compression

(arXiv, 2021-07-20) [Preprint]
Due to the high communication cost in distributed and federated learning, methods relying on compressed communication are becoming increasingly popular. Besides, the best theoretically and practically performing gradient-type methods invariably rely on some form of acceleration/momentum to reduce the number of communications (faster convergence), e.g., Nesterov's accelerated gradient descent (Nesterov, 2004) and Adam (Kingma and Ba, 2014). In order to combine the benefits of communication compression and convergence acceleration, we propose a \emph{compressed and accelerated} gradient method for distributed optimization, which we call CANITA. Our CANITA achieves the \emph{first accelerated rate} $O\bigg(\sqrt{\Big(1+\sqrt{\frac{\omega^3}{n}}\Big)\frac{L}{\epsilon}} + \omega\big(\frac{1}{\epsilon}\big)^{\frac{1}{3}}\bigg)$, which improves upon the state-of-the-art non-accelerated rate $O\left((1+\frac{\omega}{n})\frac{L}{\epsilon} + \frac{\omega^2+n}{\omega+n}\frac{1}{\epsilon}\right)$ of DIANA (Khaled et al., 2020b) for distributed general convex problems, where $\epsilon$ is the target error, $L$ is the smooth parameter of the objective, $n$ is the number of machines/devices, and $\omega$ is the compression parameter (larger $\omega$ means more compression can be applied, and no compression implies $\omega=0$). Our results show that as long as the number of devices $n$ is large (often true in distributed/federated learning), or the compression $\omega$ is not very high, CANITA achieves the faster convergence rate $O\Big(\sqrt{\frac{L}{\epsilon}}\Big)$, i.e., the number of communication rounds is $O\Big(\sqrt{\frac{L}{\epsilon}}\Big)$ (vs. $O\big(\frac{L}{\epsilon}\big)$ achieved by previous works). As a result, CANITA enjoys the advantages of both compression (compressed communication in each round) and acceleration (much fewer communication rounds).
• #### Decision trees based on 1-consequences

(Discrete Applied Mathematics, Elsevier BV, 2021-07-20) [Article]
In this paper, we study arbitrary infinite binary information systems each of which consists of an infinite set of elements and an infinite set of two-valued non-constant functions (attributes) defined on the set of elements. We consider the notion of a problem over information system, which is described by a finite number of attributes: for a given element, we should determine values of these attributes. As algorithms for problem solving, we study decision trees that use arbitrary attributes from the considered infinite set of attributes and solve the problem based on 1-consequences. In such a tree, we take into account consequences each of which follows from one equation of the kind “attribute value” obtained during the decision tree work and ignore consequences that can be derived only from at least two equations. As time complexity, we study the depth of decision trees. We prove that in the worst case, with the growth of the number of attributes in the problem description, the minimum depth of decision trees based on 1-consequences grows either as a logarithm or linearly.
• #### DMIL-IsoFun: predicting isoform function using deep multi-instance learning.

(Bioinformatics (Oxford, England), Oxford University Press (OUP), 2021-07-20) [Article]
MotivationAlternative splicing creates the considerable proteomic diversity and complexity on relatively limited genome. Proteoforms translated from alternatively spliced isoforms of a gene actually execute the biological functions of this gene, which reflect the functional knowledge of genes at a finer granular level. Recently, some computational approaches have been proposed to differentiate isoform functions using sequence and expression data. However, their performance is far from being desirable, mainly due to the imbalance and lack of annotations at isoform-level, and the difficulty of modeling gene-isoform relations.ResultWe propose a deep multi-instance learning based framework (DMIL-IsoFun) to differentiate the functions of isoforms. DMIL-IsoFun firstly introduces a multi-instance learning convolution neural network trained with isoform sequences and gene-level annotations to extract the feature vectors and initialize the annotations of isoforms, and then uses a class-imbalance Graph Convolution Network to refine the annotations of individual isoforms based on the isoform co-expression network and extracted features. Extensive experimental results show that DMIL-IsoFun improves the Smin and Fmax of state-of-the-art solutions by at least 29.6% and 40.8%. The effectiveness of DMIL-IsoFun is further confirmed on a testbed of human multiple-isoform genes, and Maize isoforms related with photosynthesis.AvailabilityThe code and data are available at http://www.sdu-idea.cn/codes.php?name=DMIL-Isofun.Supplementary informationSupplementary data are available at Bioinformatics online.
• #### BICNet: A Bayesian Approach for Estimating Task Effects on Intrinsic Connectivity Networks in fMRI Data

(arXiv, 2021-07-19) [Preprint]
Intrinsic connectivity networks (ICNs) are specific dynamic functional brain networks that are consistently found under various conditions including rest and task. Studies have shown that some stimuli actually activate intrinsic connectivity through either suppression, excitation, moderation or modification. Nevertheless, the structure of ICNs and task-related effects on ICNs are not yet fully understood. In this paper, we propose a Bayesian Intrinsic Connectivity Network (BICNet) model to identify the ICNs and quantify the task-related effects on the ICN dynamics. Using an extended Bayesian dynamic sparse latent factor model, the proposed BICNet has the following advantages: (1) it simultaneously identifies the individual ICNs and group-level ICN spatial maps; (2) it robustly identifies ICNs by jointly modeling resting-state functional magnetic resonance imaging (rfMRI) and task-related functional magnetic resonance imaging (tfMRI); (3) compared to independent component analysis (ICA)-based methods, it can quantify the difference of ICNs amplitudes across different states; (4) it automatically performs feature selection through the sparsity of the ICNs rather than ad-hoc thresholding. The proposed BICNet was applied to the rfMRI and language tfMRI data from the Human Connectome Project (HCP) and the analysis identified several ICNs related to distinct language processing functions.
• #### Fire in paradise: mesoscale simulation of wildfires

(ACM Transactions on Graphics, Association for Computing Machinery (ACM), 2021-07-19) [Article]
Resulting from changing climatic conditions, wildfires have become an existential threat across various countries around the world. The complex dynamics paired with their often rapid progression renders wildfires an often disastrous natural phenomenon that is difficult to predict and to counteract. In this paper we present a novel method for simulating wildfires with the goal to realistically capture the combustion process of individual trees and the resulting propagation of fires at the scale of forests. We rely on a state-of-the-art modeling approach for large-scale ecosystems that enables us to represent each plant as a detailed 3D geometric model. We introduce a novel mathematical formulation for the combustion process of plants - also considering effects such as heat transfer, char insulation, and mass loss - as well as for the propagation of fire through the entire ecosystem. Compared to other wildfire simulations which employ geometric representations of plants such as cones or cylinders, our detailed 3D tree models enable us to simulate the interplay of geometric variations of branching structures and the dynamics of fire and wood combustion. Our simulation runs at interactive rates and thereby provides a convenient way to explore different conditions that affect wildfires, ranging from terrain elevation profiles and ecosystem compositions to various measures against wildfires, such as cutting down trees as firebreaks, the application of fire retardant, or the simulation of rain.
• #### Multivariate Conway-Maxwell-Poisson Distribution: Sarmanov Method and Doubly-Intractable Bayesian Inference

(arXiv, 2021-07-15) [Preprint]
In this paper, a multivariate count distribution with Conway-Maxwell (COM)-Poisson marginals is proposed. To do this, we develop a modification of the Sarmanov method for constructing multivariate distributions. Our multivariate COM-Poisson (MultCOMP) model has desirable features such as (i) it admits a flexible covariance matrix allowing for both negative and positive non-diagonal entries; (ii) it overcomes the limitation of the existing bivariate COM-Poisson distributions in the literature that do not have COM-Poisson marginals; (iii) it allows for the analysis of multivariate counts and is not just limited to bivariate counts. Inferential challenges are presented by the likelihood specification as it depends on a number of intractable normalizing constants involving the model parameters. These obstacles motivate us to propose a Bayesian inferential approach where the resulting doubly-intractable posterior is dealt with via the exchange algorithm and the Grouped Independence Metropolis-Hastings algorithm. Numerical experiments based on simulations are presented to illustrate the proposed Bayesian approach. We analyze the potential of the MultCOMP model through a real data application on the numbers of goals scored by the home and away teams in the Premier League from 2018 to 2021. Here, our interest is to assess the effect of a lack of crowds during the COVID-19 pandemic on the well-known home team advantage. A MultCOMP model fit shows that there is evidence of a decreased number of goals scored by the home team, not accompanied by a reduced score from the opponent. Hence, our analysis suggests a smaller home team advantage in the absence of crowds, which agrees with the opinion of several football experts.
• #### Voltage Controlled Domain Wall Motion based Neuron and Stochastic Magnetic Tunnel Junction Synapse for Neuromorphic Computing Applications

(Institute of Electrical and Electronics Engineers (IEEE), 2021-07-15) [Preprint]
The present work discusses the proposal of a spintronic neuromorphic system with spin orbit torque driven domain wall motion-based neuron and synapse. We propose a voltage-controlled magnetic anisotropy domain wall motion based magnetic tunnel junction neuron. We investigate how the electric field at the gate (pinning site), generated by the voltage signals from pre-neurons, modulates the domain wall motion, which reflects in the non-linear switching behaviour of neuron magnetization. For the implementation of synaptic weights, we propose 3-terminal MTJ with stochastic domain wall motion in the free layer. We incorporate intrinsic pinning effects by creating triangular notches on the sides of the free layer. The pinning of domain wall and intrinsic thermal noise of device lead to the stochastic behaviour of domain wall motion. The control of this stochasticity by the spin orbit torque is shown to realize the potentiation and depression of the synaptic weight. The micromagnetics and spin transport studies in synapse and neuron are carried out by developing a coupled micromagnetic Non-Equilibrium Green’s Function (MuMag-NEGF) model. The minimization of the writing current pulse width by leveraging the thermal noise and demagnetization energy is also presented. Finally, we discuss the implementation of digit recognition by the proposed system using a spike time dependent algorithm.
• #### Bayesian calibration of order and diffusivity parameters in a fractional diffusion equation

(Journal of Physics Communications, IOP Publishing, 2021-07-15) [Article]
This work focuses on parameter calibration of a variable-diffusivity fractional diffusion model. A random, spatially-varying diffusivity field with log-normal distribution is considered. The variance and correlation length of the diffusivity field are considered uncertain parameters, and the order of the fractional sub-diffusion operator is also taken uncertain and uniformly distributed in the range (0,1). A Karhunen-Lo`eve (KL) decomposition of the random diffusivity field is used, leading to a stochastic problem defined in terms of a finite number of canonical random variables. Polynomial chaos (PC) techniques are used to express the dependence of the stochastic solution on these random variables. A non-intrusive methodology is used, and a deterministic finite-difference solver of the fractional diffusion model is utilized for this purpose. The PC surrogates are first used to assess the sensitivity of quantities of interest (QoIs) to uncertain inputs and to examine their statistics. In particular, the analysis indicates that the fractional order has a dominant effect on the variance of the QoIs considered, followed by the leading KL modes. The PC surrogates are further exploited to calibrate the uncertain parameters using a Bayesian methodology. Different setups are considered, including distributed and localized forcing functions and data consisting of either noisy observations of the solution or its first moments. In the broad range of parameters addressed, the analysis shows that the uncertain parameters having a significant impact on the variance of the solution can be reliably inferred, even from limited observations.
• #### Sex ratio at birth in Vietnam among six subnational regions during 1980–2050, estimation and probabilistic projection using a Bayesian hierarchical time series model with 2.9 million birth records

(PLOS ONE, Public Library of Science (PLoS), 2021-07-14) [Article]
The sex ratio at birth (SRB, i.e., the ratio of male to female births) in Vietnam has been imbalanced since the 2000s. Previous studies have revealed a rapid increase in the SRB over the past 15 years and the presence of important variations across regions. More recent studies suggested that the nation’s SRB may have plateaued during the 2010s. Given the lack of exhaustive birth registration data in Vietnam, it is necessary to estimate and project levels and trends in the regional SRBs in Vietnam based on a reproducible statistical approach. We compiled an extensive database on regional Vietnam SRBs based on all publicly available surveys and censuses and used a Bayesian hierarchical time series mixture model to estimate and project SRB in Vietnam by region from 1980 to 2050. The Bayesian model incorporates the uncertainties from the observations and year-by-year natural fluctuation. It includes a binary parameter to detect the existence of sex ratio transitions among Vietnamese regions. Furthermore, we model the SRB imbalance using a trapezoid function to capture the increase, stagnation, and decrease of the sex ratio transition by Vietnamese regions. The model results show that four out of six Vietnamese regions, namely, Northern Midlands and Mountain Areas, Northern Central and Central Coastal Areas, Red River Delta, and South East, have existing sex imbalances at birth. The rise in SRB in the Red River Delta was the fastest, as it took only 12 years and was more pronounced, with the SRB reaching the local maximum of 1.146 with a 95% credible interval (1.129, 1.163) in 2013. The model projections suggest that the current decade will record a sustained decline in sex imbalances at birth, and the SRB should be back to the national SRB baseline level of 1.06 in all regions by the mid-2030s.
• #### A Field Guide to Federated Optimization

(arXiv, 2021-07-14) [Preprint]
Federated learning and analytics are a distributed approach for collaboratively learning models (or statistics) from decentralized data, motivated by and designed for privacy protection. The distributed learning process can be formulated as solving federated optimization problems, which emphasize communication efficiency, data heterogeneity, compatibility with privacy and system requirements, and other constraints that are not primary considerations in other problem settings. This paper provides recommendations and guidelines on formulating, designing, evaluating and analyzing federated optimization algorithms through concrete examples and practical implementation, with a focus on conducting effective simulations to infer real-world performance. The goal of this work is not to survey the current literature, but to inspire researchers and practitioners to design federated learning algorithms that can be used in various practical applications.
• #### Spatial cluster detection with threshold quantile regression

(Environmetrics, Wiley, 2021-07-13) [Article]
Spatial cluster detection, which is the identification of spatial units adjacent in space associated with distinctive patterns of data of interest relative to background variation, is useful for discerning spatial heterogeneity in regression coefficients. Some real studies with regression-based models on air quality data show that there exists not only spatial heterogeneity but also heteroscedasticity between air pollution and its predictors. Since the low air quality is a well-known risk factor for mortality, various cardiopulmonary diseases, and preterm birth, the analysis at the tail would be of more interest than the center of air pollution distribution. In this article, we develop a spatial cluster detection approach using a threshold quantile regression model to capture the spatial heterogeneity and heteroscedasticity. We introduce two threshold variables in the quantile regression model to define a spatial cluster. The proposed test statistic for identifying the spatial cluster is the supremum of the Wald process over the space of threshold parameters. We establish the limiting distribution of the test statistic under the null hypothesis that the quantile regression coefficient is the same over the entire spatial domain at the given quantile level. The performance of our proposed method is assessed by simulation studies. The proposed method is also applied to analyze the particulate matter (PM 2.5 ) concentration and aerosol optical depth (AOD) data in the Northeastern United States in order to study geographical heterogeneity in the association between AOD and PM 2.5 at different quantile levels.
• #### Optimal Decentralized Algorithms for Saddle Point Problems over Time-Varying Networks

(arXiv, 2021-07-13) [Preprint]
Decentralized optimization methods have been in the focus of optimization community due to their scalability, increasing popularity of parallel algorithms and many applications. In this work, we study saddle point problems of sum type, where the summands are held by separate computational entities connected by a network. The network topology may change from time to time, which models real-world network malfunctions. We obtain lower complexity bounds for algorithms in this setup and develop optimal methods which meet the lower bounds.
• #### Customized Summarizations of Visual Data Collections

(Computer Graphics Forum, Wiley, 2021-07-12) [Article]
We propose a framework to generate customized summarizations of visual data collections, such as collections of images, materials, 3D shapes, and 3D scenes. We assume that the elements in the visual data collections can be mapped to a set of vectors in a feature space, in which a fitness score for each element can be defined, and we pose the problem of customized summarizations as selecting a subset of these elements. We first describe the design choices a user should be able to specify for modeling customized summarizations and propose a corresponding user interface. We then formulate the problem as a constrained optimization problem with binary variables and propose a practical and fast algorithm based on the alternating direction method of multipliers (ADMM). Our results show that our problem formulation enables a wide variety of customized summarizations, and that our solver is both significantly faster than state-of-the-art commercial integer programming solvers and produces better solutions than fast relaxation-based solvers.
• #### DES-Tcell is a knowledgebase for exploring immunology-related literature

(Scientific Reports, Springer Science and Business Media LLC, 2021-07-12) [Article]
AbstractT-cells are a subtype of white blood cells circulating throughout the body, searching for infected and abnormal cells. They have multifaceted functions that include scanning for and directly killing cells infected with intracellular pathogens, eradicating abnormal cells, orchestrating immune response by activating and helping other immune cells, memorizing encountered pathogens, and providing long-lasting protection upon recurrent infections. However, T-cells are also involved in immune responses that result in organ transplant rejection, autoimmune diseases, and some allergic diseases. To support T-cell research, we developed the DES-Tcell knowledgebase (KB). This KB incorporates text- and data-mined information that can expedite retrieval and exploration of T-cell relevant information from the large volume of published T-cell-related research. This KB enables exploration of data through concepts from 15 topic-specific dictionaries, including immunology-related genes, mutations, pathogens, and pathways. We developed three case studies using DES-Tcell, one of which validates effective retrieval of known associations by DES-Tcell. The second and third case studies focuses on concepts that are common to Grave’s disease (GD) and Hashimoto’s thyroiditis (HT). Several reports have shown that up to 20% of GD patients treated with antithyroid medication develop HT, thus suggesting a possible conversion or shift from GD to HT disease. DES-Tcell found miR-4442 links to both GD and HT, and that miR-4442 possibly targets the autoimmune disease risk factor CD6, which provides potential new knowledge derived through the use of DES-Tcell. According to our understanding, DES-Tcell is the first KB dedicated to exploring T-cell-relevant information via literature-mining, data-mining, and topic-specific dictionaries.


text:
# Math Help - Not Not B (Boolean)

1. ## Not Not B (Boolean)

Is there a way to produce a problem such as NOT A AND NOT NOT B with latex?

Edit: This is what I'm going for,

2. ## Re: Not Not B (Boolean)

Hello, Jarod_C!

Is there a way to produce a problem such as NOT A AND NOT NOT B with latex?

This is what I'm going for,

\overline{X} produces: $\overline{X}$

A\overline{B} produces: $A\overline{B}$

\overline(A\overline{B}} produces: $\overline{A\overline{B}}$


text:
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text:
# Reading a Single Qubit System Using Weak Measurement with Variable Strength

Research paper by Ahmed Younes

Indexed on: 23 Oct '16Published on: 23 Oct '16Published in: arXiv - Quantum Physics

#### Abstract

Acquiring information about an unknown qubit in a superposition of two states is essential in any computation process. Quantum measurement, or sharp measurement, is usually used to read the information contents of that unknown qubit system. Quantum measurement is an irreversible operation that makes the superposition collapses to one of the two possible states in a probabilistic way. In this paper, a quantum algorithm will be proposed to read the information in an unknown qubit without applying sharp measurement on that qubit. The proposed algorithm will use a quantum feedback control scheme by applying sharp measurement iteratively on an auxiliary qubit weakly entangled with the unknown qubit. The information contents of the unknown qubit can be read by counting the outcomes from the sharp measurement on the auxiliary qubit. Iterative measurements on the auxiliary qubit will make the amplitudes of the superposition move in a random walk manner where a weak measurement is applied on the unknown qubit which can be reversed when the random walk takes opposite steps to decrease the disturbance introduced to the system. The proposed algorithm will define the strength of the weak measurement so that it can be controlled by adding an arbitrary number of dummy qubits $\mu$ to the system. This will make the measurement process slowdown to an arbitrary scale so that the effect of the sharp measurement on the unknown qubit is reached after $O(\mu^2)$ measurements on the auxiliary qubit.


text: We have already provided detailed study notes or revision notes for this unit, which you can easily download by registering yourself on Vedantu website. Hydroxides (OH â) are insoluble or slightly soluble except for the hydroxides of the alkalis (because of Rule 1). Given that the ionic product of $Ni(OH)_2$ is $2 \times 10^{-15}$. A human body contains approximately 0.12% of Na and 0.25% of K. Sodium ions are found in blood plasma and interstitial fluid. The volume strength of $3.0\, N\, H_2O_2$ is, Non-stoichiometric hydrides are formed by, The correct order of solubility of the sulphates of alkaline earth metals in water is $Be > Mg > Ca > Sr > Ba$. 9:31 Used as laboratory reagent in various experiments. Other alkali metals do not form hydrates. Chlorides of both are deliquescent but their hydrates (LiCl.2H2O and MgCl2.8H2O) are crystalline solids. Alkaline earth metals react with acids and releases hydrogen gas. Compare the solubility and thermal stability of the following compounds of the alkali metals with those of the alkaline earth metals. Beryllium hydroxide and aluminium hydroxide both give beryllium ion and aluminium ion respectively on dissolving in excess of aqueous solution of base. Of the following, which species is primarily obtained in a solution containing $KHF_2$ ? Oxides and hydroxides of Li and Mg are less soluble in water and decompose on heating. Alkali metals react with air and form their oxides. Compounds of other alkaline earth metals are ionic in nature. Lithium hydrogen carbonate is found in solution form. Note – Li reacts with H2 at 1073K temperature. The explanation for the trends in solubility is given in chapter 3.17 enthalpies of solution The pH of an aqueous solution of a hydroxide depends on the extent to which the metal hydroxide can be split to produce independent ions. - The solubility of the alkaline earth metal sulphates is slightly increased by the addition of strong acids. Carbonates of alkaline earth metals are water insoluble. Beryllium carbonate is unstable and should be kept in the atmosphere of CO2. All other alkali metals are more reactive than Li. It is used in baking as it decomposes on heating and generates carbon dioxide which makes the baked dishes spongy. It is highly soluble in water. The carbonates of alkaline earth metals can be regarded as salts of weak carbonic acid (H2CO3) and metal hydroxide, M (OH)2. Alkali metal sulphates are more soluble in water than alkaline earth metals. Used for the preparation of pure fats and oils. Nitrates of alkaline earth metals are formed by dissolution of the carbonates in dil. These can be precipitated by addition of ammonium carbonate and sodium carbonate. The elements of group 1 are known as alkali metals because their oxides and hydroxides are basic in nature. Biological Importance of Magnesium and Calcium, Magnesium and calcium are the elements of the group 1 which has biological importance. Solubility of the carbonates The carbonates tend to become less soluble as you go down the Group. Calcium is necessary for our healthy bones. Which one of the following has maximum lattice energy? These oxides react with moisture and form hydroxides. Oxide of beryllium is amphoteric in nature. M+(dissolved in ammonia) + e- + NH3 MNH2 + 1/2H2. Compare the solubility and thermal stability of the following compounds of the alkali metals with those of the alkaline earth metals. Simple :-In the case of S block element we will see the difference in sizeof cation and anion i.e. All alkaline earth metals are strong reducing agents but weaker than alkali metals. Some similarities between the are listed below –. Hydrogen carbonates of other alkali metals are found in solid state. If we consider the periodic table, the elements that would fall in the group 2 of the table are usually known as alkali earth metals. They react with dihydrogen and form their respective hydrides. Used in preparation of mortar and bleaching powder. The greater the ease of producing OH-ions, the more alkaline is the The reaction occurs at 673K temperature. Solubility of sodium carbonate and calcium carbonate are 30.7 g/100 g water and 0.0013/100 g respectively at 25 0 C. You can see the difference of values. Beryllium hydroxide is amphoteric in nature. These salts are soluble in water and thermally stable. Sodium ions also help in activation of various enzymes. HNO3. Solubility, thermal stability and basic character of hydroxides of alkaline earth metals increases from Mg to Ba due to increase in atomic size. Lithium shows diagonal relationship with magnesium. All alkaline metals react with halogens and form ionic halides. The term "thermal decomposition" describes splitting up a compound by heating it. Solubility of sulphates of alkaline earth metals decreases as we move down the group. Note – Their hydrides are saline in nature. BeO is being an exception is covalent in nature. (a) Nitrates (b) Carbonates (c) Sulphates. Similarities Between Li and Mg– Lithium shows diagonal relationship with magnesium. Almost 25g of Mg is found in the body of an adult human being. They follow the following trend – F- > Cl- > Br- > I-. Their biological importance can be described by the following points –. Note - Alkali metals form deep blue - black colored solution with ammonia. They react with dihydrogen and forms their respective hydrides. Only Be and Mg react with N2 directly. Beryllium sulphate is readily soluble in water. By reaction of calcium chloride and sodium carbonate. Pro Lite, Vedantu Milk of lime – Suspension of calcium hydroxide in water. Its aqueous solution reacts with carbon dioxide and gives sodium carbonate. Solubility and thermal stability of carbonates of alkaline earth metals increases on moving down the group due increase in the size of metal ions. Group 2, Alkaline Earth Metals. The alkaline earth metals are the elements that correspond to group 2 of the modern periodic table. Except BeO, all other alkaline earth metal oxides are basic in nature and form their respective hydroxides with water. Sulphates of alkaline earth metals are white crystalline solids and thermally stable. Beryllium and magnesium sulphates are readily soluble in water due to their high hydration enthalpies. This is due to the fact that the lattice energy decreases down the group due to increase in size of the alkaline earth metals cation whereas the hydration energy of the cation â¦ Used in the purification process of bauxite. In vapor phase chlorides of both Al and Be show chloride bridge structure. Superoxides are either yellow or orange in color and paramagnetic in nature. Which alkali metal during flame test will show colour corresponding to maximum wavelength? Characteristics of the Compounds of Alkaline Earth Metals. The solubility of the alkaline earth metal hydroxides in water increases with increase in atomic number down the group. In Wolff‐Kishner reduction, the carbonyl group of aldehydes and ketones is converted into. The elements of group 2 are known as alkaline earth metals because their oxides and hydroxides are basic in nature and these metals are found in earth or earth’s crust. All the alkaline earth metals combine directly with the halogens at appropriate temperature forming halides, where stands for alkaline earth metals. Lithium fluoride is much less soluble in water than other alkali fluorides. Carbonates of alkaline earth metals are insoluble in water. (ii) Carbonates of alkaline earth metals decompose on heating to form corresponding oxide and carbon dioxide. The atomic radiusis: Find out the solubility of $Ni(OH)_2$ in 0.1 M NaOH. All the carbonates of alkaline earth metal are more soluble in the presence of CO2 due to the formation of corresponding bicarbonates. All the Group 2 carbonates and their resulting oxides exist as white solids. Hydroxides of alkaline earth metals are less basic and stable than hydroxides of alkali metals. Only Be and Mg react with N, General Characteristics of Compounds of the Alkaline Earth Metals, Halides of all alkaline earth metals are ionic in nature, except BeX, Beryllium carbonate is unstable and should be kept in the atmosphere of CO, Solubility of sulphates of alkaline earth metals decreases as we move down the group. on Vedantu website. Also, the solubility increases as we move down the group. By electrolysis method – It is prepared by electrolysis of brine solution (conc. The hydroxides of alkaline earth metals therefore come under weak base category. The heat of formation of the reaction, $\ce{ SO_{2} +\frac{1}{2}O_{2} -> SO_3}$ will be. But carbonates of alkaline earth metals are insoluble in water. All the Group 2 carbonates are very sparingly soluble. Used in toothpaste, chewing gum, cosmetic materials. Note – M can be any alkaline earth metal. Note – Calcium chloride is hygroscopic in nature and on exposure to air, it absorbs water and forms a solution. It is used as an antiseptic for skin infections. Halides of all alkaline earth metals are ionic in nature, except BeX2, The tendency of forming halide hydrates decreases on moving down the group (from Mg to Ba). Lithium is harder and lighter than other alkali metals. All alkali metals can be dissolved in liquid ammonia. On heating, it loses its water of crystallization and forms its anhydrous form which is called ‘dead burnt plaster’. (i) the carbonates/phosphates/sulfides of the alkalis (because of Rule 1), and (ii) ammonium carbonate/phosphate/sulfide (because of Rule 2). Sodium hydroxide General name – Caustic soda. Alkali metal hydrides show high melting points as they are ionic solids. Let us discuss the characteristics of the compounds of the alkali earth metals. Each of these elements contains two electrons in their outermost shell. Used in glass making, purification of sugar and tanning industry. All alkali metals can be dissolved in liquid ammonia. 5.2 Alkali metals: The word âalkaliâ is derived from the word al-qalÄ«y meaning the plant ashes, referring to the original source of alkaline substances. Other alkali metals react with ethyne and form corresponding ethynide. Solubility and Stability of Carbonates and Sulphates Carbonates. Used in the production of sodium oxide, caustic soda, sodium carbonate. Aqueous solution of their oxides and hydroxides turn red litmus paper into blue. Pro Lite, CBSE Previous Year Question Paper for Class 10, CBSE Previous Year Question Paper for Class 12. Ions of both form complexes such as BeF42-, AlF63- etc. We hope after reading this article you will be able to solve problems based on the topic. On electrolysis of dil.sulphuric acid using Platinum (Pt) electrode, the product obtained at anode will be: An element has a body centered cubic (bcc) structure with a cell edge of 288 pm. Magnesium is important for various enzymes involved in the utilization of energy (ATP). On decomposition, lithium nitrate gives lithium oxide. These hydroxides evolve a large amount of heat when dissolved in water. The carbonates become less soluble down the group. 5:49 Compare the solubility and thermal stability of the following compounds of the alkali metals with those of the alkaline earth metals. Sodium – potassium pump which operates across the cell membrane is based on the sodium and potassium ions. Chlorides of both are deliquescent but their hydrates (LiCl.2H, All alkaline earth metals do not react with nitrogen directly. Note – Be and Mg on reaction with air can form nitrides directly if enough amount of nitrogen is present in the air in the area. Melting and boiling points of alkali metal halides depend on the halogen ion. Compounds of other alkaline do not get hydrolyzed easily. (v) The carbonates and sulphates of alkaline earth metals all decompose on heating but the temperature of their decomposition increases down the group, i.e., their thermal stability increases. Note – Alkaline earth metals are less reactive than alkali metals, although reactivity of alkaline earth metals increases on moving down the group. Solubility and basicity of hydroxides: They are less soluble and less basic than alkali metal hydroxides. It is the strongest reducing agent among alkali metals. It is one of the reagents used in textile, paint and paper industries. Solubilities of the halides, nitrates, carbonates, sulfates, and some perchlorates of all the alkali metals and alkaline earth metals in methanol at room temperature have been determined. Which among the following elements of group-2 exhibits anomalous properties ? Here in this article we have discussed the unit in a summarized way with the emphasis on important topics of the unit. Data on some, such as cesium and rubidium fluoride, nitrate, carbonate, and sulfate, appear to be reported for the first time. Their solubility decreases on moving down the group going down the group the lattice energies of carbonates do not decrease more readily while the hydration energy of the metal ions decrease very much leading to decreased solubility. This is because, The values of heat of formation of $\ce{SO_2}$ and $\ce{SO_3}$ are $\ce{- 298.2 \, kJ}$ and $\ce{- 98.2\, kJ}$. These oxides possess high enthalpy of formation. Sodium ions help in transporting the signals from nerve cells, regulating the water flow across cell membranes, transport of sugars and amino acids to cells. Beryllium carbonate is unstable in nature. lithium chloride is deliquescent while in its hydrate form, it’s a crystalline solid. Decreases on moving from top to bottom in the group due to increase in size. Pro Lite, Vedantu The alkaline earth metals are somewhat easier to isolate from their ores, as compared to the alkali metals, because their carbonate and some sulfate and hydroxide salts â¦ None of the carbonates is anything more than very sparingly soluble. All alkaline earth metals do not react with nitrogen directly. At high temperatures, it decomposes to give calcium oxide and carbon dioxide. Its chloride (LiCl) forms hydrate (LiCl.2H2O). Decreases on moving from top to bottom in the group. All alkali metals are strong reducing agents. Almost 1200g of calcium is found in the body of an adult. Earlier, in this tutorial, you learnt, solubility of alkaline earth metals is very low compared to the alkali metals. The carbonates of alkaline earth metals are sparingly soluble in water. (v) Carbonates and sulphates of Li decompose on heating while the stability, of carbonates and sulphates of other metals increases down the group. Mg reacts with alkyl halide through an insertion reaction or combination reaction. Reaction between acetone and methyl magnesium chloride followed by hydrolysis will give : Identify the correct statements from the following: Which of the following set of molecules will have zero dipole moment ? Increases on moving from top to bottom in the group, Decreases on moving from top to bottom in the group, Elements of the First Group – Physical Properties, Increases on moving from top to bottom in the group (Exception – K-shows lower density), Elements of the First Group – Chemical Properties. Classification of Elements and Periodicity in Properties. Beryllium hydroxide is amphoteric in nature which means it reacts with acid and base both. They are important minerals of our body. (A) BaCO3 > SrCO3 > CaCO3 > MgCO3 (B) MgCO3 > CaCO3 > This ends our coverage on the summary of the unit “The s-block elements”. 2NaHg (sodium amalgam) + 2H2O 2NaOH + 2Hg + H2. (a) Nitrates (b) Carbonates (c) Sulphates Answer: (a) Nitrates of both group 1 and group 2 elements are soluble in water because hydration energy is more than the lattice energy. Here we shall look at the solubilities of the hydroxides and sulfates of Group 2 metals. Similarities Between Be and Al – Beryllium shows diagonal relationship with aluminum. Alkaline earth metals react with air and form their oxides. Which of the following is the weakest base? For example,Li2CO3 +heat -> Li2O +CO2MgCO3 +Heat -> MgO +CO2Na2CO3 +heat -> no effect.The stabilities of carbonates of alkaline earth metals increase on â¦ Crystalline form of magnesium nitrate has six crystallization of water molecules.


text:
## Electronic Journal of Probability

### A Gaussian limit process for optimal FIND algorithms

#### Abstract

We consider versions of the FIND algorithm where the pivot element used is the median of a subset chosen uniformly at random from the data. For the median selection we assume that subsamples of size asymptotic to $c \cdot n^\alpha$ are chosen, where $0 < \alpha \leq \frac{1}{2}$, $c > 0$ and $n$ is the size of the data set to be split. We consider the complexity of FIND as a process in the rank to be selected and measured by the number of key comparisons required. After normalization we show weak convergence of the complexity to a centered Gaussian process as $n \to \infty$, which depends on $\alpha$. The proof relies on a contraction argument for probability distributions on càdlàg functions. We also identify the covariance function of the Gaussian limit process and discuss path and tail properties.

#### Article information

Source
Electron. J. Probab., Volume 19 (2014), paper no. 3, 28 pp.

Dates
Accepted: 6 January 2014
First available in Project Euclid: 4 June 2016

https://projecteuclid.org/euclid.ejp/1465065645

Digital Object Identifier
doi:10.1214/EJP.v19-2933

Mathematical Reviews number (MathSciNet)
MR3164756

Zentralblatt MATH identifier
1358.68085

Rights

#### Citation

Sulzbach, Henning; Neininger, Ralph; Drmota, Michael. A Gaussian limit process for optimal FIND algorithms. Electron. J. Probab. 19 (2014), paper no. 3, 28 pp. doi:10.1214/EJP.v19-2933. https://projecteuclid.org/euclid.ejp/1465065645

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• Mörters, Peter; Peres, Yuval. Brownian motion. With an appendix by Oded Schramm and Wendelin Werner. Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge University Press, Cambridge, 2010. xii+403 pp. ISBN: 978-0-521-76018-8
• Neininger, Ralph; Rüschendorf, Ludger. A general limit theorem for recursive algorithms and combinatorial structures. Ann. Appl. Probab. 14 (2004), no. 1, 378–418.
• Neininger, Ralph; Rüschendorf, Ludger. Analysis of algorithms by the contraction method: additive and max-recursive sequences. Interacting stochastic systems, 435–450, Springer, Berlin, 2005.
• Neininger, R. and Sulzbach, H.: On a functional contraction method. arXiv:1202.1370
• Paulsen, Volkert. The moments of FIND. J. Appl. Probab. 34 (1997), no. 4, 1079–1082.
• Ragab, M.: Partial Quicksort and weighted branching processes. Dissertation, Christian-Albrechts-Universität zu Kiel, (2011). Electronically available via urn:nbn:de:gbv:8-diss-73701
• Ragab, Mahmoud; Roesler, Uwe. The Quicksort process. Stochastic Process. Appl. 124 (2014), no. 2, 1036–1054.
• Rösler, Uwe. A limit theorem for "Quicksort". RAIRO Inform. Théor. Appl. 25 (1991), no. 1, 85–100.
• Rösler, U.: Quickselect revisited. J. Iranian Stat. Soc. 3, (2004), 271–296.
• Rösler, U.; RÃ¼schendorf, L. The contraction method for recursive algorithms. Average-case analysis of algorithms (Princeton, NJ, 1998). Algorithmica 29 (2001), no. 1-2, 3–33.
• Rüschendorf, Ludger. On stochastic recursive equations of sum and max type. J. Appl. Probab. 43 (2006), no. 3, 687–703.
• Sulzbach, H.: On a Functional Contraction Method. Dissertation, Goethe-Universität Frankfurt am Main, (2012). Electronically available via urn:nbn:de:hebis:30:3-248587
• Talagrand, Michel. Regularity of Gaussian processes. Acta Math. 159 (1987), no. 1-2, 99–149.
• Vallée, Brigitte; Clément, Julien; Fill, James Allen; Flajolet, Philippe. The number of symbol comparisons in QuickSort and QuickSelect. Automata, languages and programming. Part I, 750–763, Lecture Notes in Comput. Sci., 5555, Springer, Berlin, 2009.
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# Predicate Logic and Popular Culture (Part 183): Avengers

Let $p$ be the proposition “The city is flying,” let $q$ be the proposition “We’re fighting an army of robots,” and let $r$ be the proposition “I have a bow and arrow.” Translate the logical statement

$p \land q \land r$.

This matches a memorable line from “Avengers: Age of Ultron.”

Context: Part of the discrete mathematics course includes an introduction to predicate and propositional logic for our math majors. As you can probably guess from their names, students tend to think these concepts are dry and uninteresting even though they’re very important for their development as math majors.

In an effort to making these topics more appealing, I spent a few days mining the depths of popular culture in a (likely futile) attempt to make these ideas more interesting to my students. In this series, I’d like to share what I found. Naturally, the sources that I found have varying levels of complexity, which is appropriate for students who are first learning prepositional and predicate logic.

When I actually presented these in class, I either presented the logical statement and had my class guess the statement in actual English, or I gave my students the famous quote and them translate it into predicate logic. However, for the purposes of this series, I’ll just present the statement in predicate logic first.

# Predicate Logic and Popular Culture (Part 182): Moana

Let $P$ be the set of all people, let $L(x)$ be the proposition “$x$ is on this island,” and let $K(x)$ be the proposition “I know $x$.” Translate the logical statement

$\forall x \in P(L(x) \Rightarrow K(x))$.

This matches a line from Disney’s “Moana.”

Context: Part of the discrete mathematics course includes an introduction to predicate and propositional logic for our math majors. As you can probably guess from their names, students tend to think these concepts are dry and uninteresting even though they’re very important for their development as math majors.

In an effort to making these topics more appealing, I spent a few days mining the depths of popular culture in a (likely futile) attempt to make these ideas more interesting to my students. In this series, I’d like to share what I found. Naturally, the sources that I found have varying levels of complexity, which is appropriate for students who are first learning prepositional and predicate logic.

When I actually presented these in class, I either presented the logical statement and had my class guess the statement in actual English, or I gave my students the famous quote and them translate it into predicate logic. However, for the purposes of this series, I’ll just present the statement in predicate logic first.

# Predicate Logic and Popular Culture (Part 181): Charlie Puth

Let $T(t)$ be the proposition “We talk at time $t$.” Translate the logical statement

$\forall t>0( \lnot T(t) )$.

This matches the hit song by Charlie Puth.

Context: Part of the discrete mathematics course includes an introduction to predicate and propositional logic for our math majors. As you can probably guess from their names, students tend to think these concepts are dry and uninteresting even though they’re very important for their development as math majors.

In an effort to making these topics more appealing, I spent a few days mining the depths of popular culture in a (likely futile) attempt to make these ideas more interesting to my students. In this series, I’d like to share what I found. Naturally, the sources that I found have varying levels of complexity, which is appropriate for students who are first learning prepositional and predicate logic.

When I actually presented these in class, I either presented the logical statement and had my class guess the statement in actual English, or I gave my students the famous quote and them translate it into predicate logic. However, for the purposes of this series, I’ll just present the statement in predicate logic first.

# Predicate Logic and Popular Culture (Part 180): Queen

Let $p$ be the proposition “I’m just a poor boy,” let $P$ be the set of all people, and let $L(x)$ be the proposition “$x$ loves me.” Translate the logical statement

$p \land \forall x in P( \lnot L(x) )$.

This matches a line from “Bohemian Rhapsody.”

Context: Part of the discrete mathematics course includes an introduction to predicate and propositional logic for our math majors. As you can probably guess from their names, students tend to think these concepts are dry and uninteresting even though they’re very important for their development as math majors.

In an effort to making these topics more appealing, I spent a few days mining the depths of popular culture in a (likely futile) attempt to make these ideas more interesting to my students. In this series, I’d like to share what I found. Naturally, the sources that I found have varying levels of complexity, which is appropriate for students who are first learning prepositional and predicate logic.

When I actually presented these in class, I either presented the logical statement and had my class guess the statement in actual English, or I gave my students the famous quote and them translate it into predicate logic. However, for the purposes of this series, I’ll just present the statement in predicate logic first.

# Predicate Logic and Popular Culture (Part 179): Harry Potter

Let $P$ be the set of all people, let $W(x)$ be the proposition “$x$ is a witch,” let $Z(x)$ be the proposition “$x$ is a wizard,” let $B(x)$ be the proposition “$x$ went bad,” and let $S(x)$ be the proposition “$x$ was in Slytherin.” Translate the logical statement

$\lnot \exists x \in P( (W(x) \lor Z(x)) \land B(x) \land ~S(x))$.

This matches matches a line from “Harry Potter and the Sorcerer’s Stone.”

Context: Part of the discrete mathematics course includes an introduction to predicate and propositional logic for our math majors. As you can probably guess from their names, students tend to think these concepts are dry and uninteresting even though they’re very important for their development as math majors.

In an effort to making these topics more appealing, I spent a few days mining the depths of popular culture in a (likely futile) attempt to make these ideas more interesting to my students. In this series, I’d like to share what I found. Naturally, the sources that I found have varying levels of complexity, which is appropriate for students who are first learning prepositional and predicate logic.

When I actually presented these in class, I either presented the logical statement and had my class guess the statement in actual English, or I gave my students the famous quote and them translate it into predicate logic. However, for the purposes of this series, I’ll just present the statement in predicate logic first.

# Predicate Logic and Popular Culture (Part 178): Lauryn Hill

Let $P$ be the set of all people, and let $f(x)$ measure how much $x$ loves you.

$\lnot \exists x in P(f(x) > f(I))$.

This matches matches a line from “Ex Factor.” This is also a nice exercise in predicate logic, as the statement is also logically equivalent to

$\forall x in P(f(x) \le f(I))$.

Context: Part of the discrete mathematics course includes an introduction to predicate and propositional logic for our math majors. As you can probably guess from their names, students tend to think these concepts are dry and uninteresting even though they’re very important for their development as math majors.

In an effort to making these topics more appealing, I spent a few days mining the depths of popular culture in a (likely futile) attempt to make these ideas more interesting to my students. In this series, I’d like to share what I found. Naturally, the sources that I found have varying levels of complexity, which is appropriate for students who are first learning prepositional and predicate logic.

When I actually presented these in class, I either presented the logical statement and had my class guess the statement in actual English, or I gave my students the famous quote and them translate it into predicate logic. However, for the purposes of this series, I’ll just present the statement in predicate logic first.

# Predicate Logic and Popular Culture (Part 177): Shakira

Let $P$ be the set of all people, let $L(x)$ be the proposition “$x$ learns,” and let $W(x)$ be the proposition “$x$ gets it wrong.” Translate the logical statement

$\lnot \exists x \in P(L(x) \land \lnot W(x))$.

This matches this quote from “Try Everything” from “Zootopia.” This is also a nice exercise in predicate logic, as the statement is also logically equivalent to

$\forall x \in P(\lnot L(x) \lor W(x))$

or

$\forall x \in P(L(x) \Rightarrow W(x))$.

Context: Part of the discrete mathematics course includes an introduction to predicate and propositional logic for our math majors. As you can probably guess from their names, students tend to think these concepts are dry and uninteresting even though they’re very important for their development as math majors.

In an effort to making these topics more appealing, I spent a few days mining the depths of popular culture in a (likely futile) attempt to make these ideas more interesting to my students. In this series, I’d like to share what I found. Naturally, the sources that I found have varying levels of complexity, which is appropriate for students who are first learning prepositional and predicate logic.

When I actually presented these in class, I either presented the logical statement and had my class guess the statement in actual English, or I gave my students the famous quote and them translate it into predicate logic. However, for the purposes of this series, I’ll just present the statement in predicate logic first.

# Predicate Logic and Popular Culture (Part 176): Game of Thrones

Let $p$ be the proposition “You play the game of thrones,” let $q$ be the proposition “You win,” and let $r$ be the proposition “You die.” Translate the logical statement

$p \Rightarrow (q \lor r)$.

This matches this quote from “Game of Thrones.”

Context: Part of the discrete mathematics course includes an introduction to predicate and propositional logic for our math majors. As you can probably guess from their names, students tend to think these concepts are dry and uninteresting even though they’re very important for their development as math majors.

In an effort to making these topics more appealing, I spent a few days mining the depths of popular culture in a (likely futile) attempt to make these ideas more interesting to my students. In this series, I’d like to share what I found. Naturally, the sources that I found have varying levels of complexity, which is appropriate for students who are first learning prepositional and predicate logic.

When I actually presented these in class, I either presented the logical statement and had my class guess the statement in actual English, or I gave my students the famous quote and them translate it into predicate logic. However, for the purposes of this series, I’ll just present the statement in predicate logic first.

# Predicate Logic and Popular Culture (Part 175): Diana Ross and the Supremes

Let $T(t)$ be the proposition “We are together at time $t$.” Translate the logical statement

$\exists t > 0 (T(t))$.

This matches this classic by Diana Ross and the Supremes.

Context: Part of the discrete mathematics course includes an introduction to predicate and propositional logic for our math majors. As you can probably guess from their names, students tend to think these concepts are dry and uninteresting even though they’re very important for their development as math majors.

In an effort to making these topics more appealing, I spent a few days mining the depths of popular culture in a (likely futile) attempt to make these ideas more interesting to my students. In this series, I’d like to share what I found. Naturally, the sources that I found have varying levels of complexity, which is appropriate for students who are first learning prepositional and predicate logic.

When I actually presented these in class, I either presented the logical statement and had my class guess the statement in actual English, or I gave my students the famous quote and them translate it into predicate logic. However, for the purposes of this series, I’ll just present the statement in predicate logic first.

# Predicate Logic and Popular Culture (Part 174): Rocky IV

Let $p$ be the proposition “He dies.” Translate the logical statement

$p \Rightarrow p$.

This famous tautology was uttered by Ivan Drago in Rocky IV.

Context: Part of the discrete mathematics course includes an introduction to predicate and propositional logic for our math majors. As you can probably guess from their names, students tend to think these concepts are dry and uninteresting even though they’re very important for their development as math majors.

In an effort to making these topics more appealing, I spent a few days mining the depths of popular culture in a (likely futile) attempt to make these ideas more interesting to my students. In this series, I’d like to share what I found. Naturally, the sources that I found have varying levels of complexity, which is appropriate for students who are first learning prepositional and predicate logic.

When I actually presented these in class, I either presented the logical statement and had my class guess the statement in actual English, or I gave my students the famous quote and them translate it into predicate logic. However, for the purposes of this series, I’ll just present the statement in predicate logic first.


text:
April 1, 2019

# Easily Add LaTex Math to a Ghost Blog

This is a guide to get LaTex math to work on a Ghost Blog. I chose a fast JavaScript Library developed by Khan Academy called KaTex. To see it in action, check my previous blog post on P-NP. Here are the steps to get it working:

1. Login to the Ghost Administration Panel, and click the "Code Injection" tab on the sidebar.

2. Paste in the following code block into the "Blog Header" section and Save:

<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.10.1/dist/katex.css" crossorigin="anonymous">
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.10.1/dist/katex.js" crossorigin="anonymous"></script>

For inline equations, simply surround the LaTex math with a backslash and parentheses: $$LaTex_HERE$$. Example: $$\sum_{i=1}^{n}{n} = \frac{n(n-1)}{2}$$. To get a large and centred expression, surround the LaTex math with a backslash and square brackets: $LaTex_HERE$. Example: $\mathcal L_{\mathcal T}(\vec{\lambda}) = \sum_{(\mathbf{x},\mathbf{s})\in \mathcal T} \log P(\mathbf{s}\mid\mathbf{x}) - \sum_{i=1}^m \frac{\lambda_i^2}{2\sigma^2}$
In Markdown, you will have to escape some of the control characters, as explained here. Usually, all that needs to be escaped are the surrounding backslashes. To get the same expressions as above, surround the LaTex with double backslashes: \$$LaTex_HERE \$$ and \$LaTex_HERE \$.


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How to find CDF on disk [duplicate]

Let $Z = (X, Y)$ be a random variable uniform inside circle of radius $R$. How to find cumulative distribution function (CDF) on disk?

marked as duplicate by Did, Graham Kemp probability StackExchange.ready(function() { if (StackExchange.options.isMobile) return; $('.dupe-hammer-message-hover:not(.hover-bound)').each(function() { var$hover = $(this).addClass('hover-bound'),$msg = $hover.siblings('.dupe-hammer-message');$hover.hover( function() { $hover.showInfoMessage('', { messageElement:$msg.clone().show(), transient: false, position: { my: 'bottom left', at: 'top center', offsetTop: -7 }, dismissable: false, relativeToBody: true }); }, function() { StackExchange.helpers.removeMessages(); } ); }); }); Sep 27 '16 at 12:26

• Self-duplicate of math.stackexchange.com/q/1931107 Please stop that. – Did Sep 27 '16 at 11:56
• I reopened because the question was closed and I modified completely,but don't reopened. – Wagner Jorge Sep 27 '16 at 16:21
• Yes, and this is called cheating the system, so: Please stop. – Did Sep 27 '16 at 18:40
• I don't had knowledge, sorry. Please delete the question. I don't have the intention of to use cheat of system. I repeat I don't had knowledge. You can delete this question. Thank you for your help. – Wagner Jorge Sep 27 '16 at 20:03

$$P(X<x,Y<y)=\frac{\text{red area(x,y)}}{R^2\pi}$$


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## Chemistry (7th Edition)

Time, t= 20.0 min= $(20.0\times60)s$= 1200 s Current, I= 2.40 A Charge=$I\times t$=$2.40 A\times 1200 s$= 2880 C According to the reaction: $Ag^{+}+ e^{-}→Ag$ we require 1F or 96487 C to deposit 1 mol or 107.87 g of Ag at the cathode. For 2880 C, the mass of Ag obtained= $\frac{107.87gmol^{-1}\times2880 C}{1\times96487Cmol^{-1}}$ = 3.22 g


text:
# The Penrose–Lucas argument

I was looking at the Penrose–Lucas argument as discussed on Wikipedia. It states:

In 1931, the mathematician and logician Kurt Gödel proved that any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete. Further to that, for any consistent formal theory that proves certain basic arithmetic truths, there is an arithmetical statement that is true, but not provable in the theory.

In his first book on consciousness, The Emperor's New Mind (1989), Penrose made Gödel's theorem the basis of what quickly became an intensely controversial claim. He argued that while a formal proof system cannot, because of the theorem, prove its own incompleteness, Gödel-type results are provable by human mathematicians. He takes this disparity to mean that human mathematicians are not describable as formal proof systems, and are not therefore running an algorithm.

If find this hard to believe, because I can't see why either one of the following is true:

(1) Humans are proving incompleteness not using the system itself, but using some greater system
OR
(2) If there is a proof of incompleteness that was found in the system by a human, then as long as that proof is of finite length, it could be found algorithmically simply by trying and checking every proof until one finds one which is correct.

I looked at the criticisms on the Wikipedia page, and they only criticised the science of quantum effects in the brain, not the mathematics of the original assertion.

I'm sure I'm missing something, but is his original assertion correct? And if so, could you explain why?

-
I think this question would be better suited for Philosophy.SE –  Mahmud Jul 2 '12 at 3:05
Mahmud: I'm more interested in the mathematics behind the statement, as in whether certain proofs can not be generated by an algorithm. I believe that's purely a mathematical question, not a philosophy one. –  Clinton Jul 2 '12 at 3:17
Of course it is not correct. One can program a computer to prove Gödel-type results. –  André Nicolas Jul 2 '12 at 3:57
I heard Penrose speak about this back around the time the book came out, and I thought he was misunderstanding the mathematics badly, and for essentially the reasons you give. –  Gerry Myerson Jul 2 '12 at 3:57


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# 井上　順子

## Research

### Research interests:

Lie groups and their representations. I am interested in representation theory of nilpotent and solvable Lie groups and harmonic analysis of homogeneous spaces.

### Conference Program (organized)

• Representation theory and harmonic analysis on homogeneous spaces --- Japanese / English

### Selected publications

• (with J. Ludwig) Characterization of certain spaces of $C^{\infty}$-vectors of irreducible representations of solvable Lie groups. RIMS Kokyuroku Bessatsu B7, 177-185 (2008). MSC2000: *22E27 22E25 43A85
• (with J. Ludwig) $C^{\infty}$-vectors of irreducible representations of exponential solvable Lie groups. J. Math. Soc. Japan 59, No. 4, 1081-1103 (2007). MSC2000: *22E27 22E25 43A85   Article
• Holomorphically induced representations of some solvable Lie groups. J. Funct. Anal. 186, No.2, 269-328 (2001). MSC2000: *22E27 22E30 22E25   Article
• Semiinvariant vectors associated to decompositions of monomial representations of exponential Lie groups, J. Math. Soc. Japan,Vol.49 (1997), 647-661. MSC2000: *22E27 22E30   Article
• Lp-Fourier transforms for solvable Lie groups acting on Siegel domains, Pacific J. Math.,Vol 155 (1992), 295-318. MSC2000: *43A32 22E27 43A15   Article
• Fourier transforms for affine automorphism groups on Siegel domains, J. Math. Soc. Japan, Vol. 43 (1991), 248-259. MSC2000: *22E30 22E27 43A30   Article
• Monomial Representations of Certain Exponential Lie Groups, J. Funct. Anal., Vol. 83 (1989), 121--149.   Article

# 井上　順子

Associate Professor of Mathematics
University Education Center
Tottori University
Tottori 680-8550, JAPAN